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MCQ (Single Correct Answer)

1

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is $P \times 10^{11} \, \text{Nm}^{-2}$, where the value of $P$ is: (Take $g = 3\pi \, \text{m/s}^2$)

JEE Main 2025 (Online) 8th April Evening Shift
2

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle ≈ 0°) with 30° inclined with the vertical. The length of water risen in the capillary is _______ cm. (Take $g = 9.8 \text{ m/s}^2$)

JEE Main 2025 (Online) 7th April Evening Shift
3

Two wires A and B are made of same material having ratio of lengths $\frac{L_A}{L_B}=\frac{1}{3}$ and their diameters ratio $\frac{d_A}{d_B}=2$. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

JEE Main 2025 (Online) 7th April Morning Shift
4

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of $10^5 \mathrm{~N}$ at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement $\theta$ of the rod axis from its original position would be : (shear moduli, $G=10^{10} \mathrm{~N} / \mathrm{m}^2$ )

JEE Main 2025 (Online) 4th April Evening Shift
5

Two liquids $A$ and $B$ have $\theta_A$ and $\theta_B$ as contact angles in a capillary tube. If $K=\cos \theta_A / \cos \theta_B$, then identify the correct statement:

JEE Main 2025 (Online) 4th April Morning Shift
6
Two cylindrical vessels of equal cross sectional area of $2 \mathrm{~m}^2$ contain water upto heights 10 m and 6 m , respectively. If the vessels are connected at their bottom then the work done by the force of gravity is (Density of water is $10^3 \mathrm{~kg} / \mathrm{m}^3$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
JEE Main 2025 (Online) 3rd April Evening Shift
7

A solid steel ball of diameter 3.6 mm acquired terminal velocity $2.45 \times 10^{-2} \mathrm{~m} / \mathrm{s}$ while falling under gravity through an oil of density $925 \mathrm{~kg} \mathrm{~m}^{-3}$. Take density of steel as $7825 \mathrm{~kg} \mathrm{~m}^{-3}$ and g as $9.8 \mathrm{~m} / \mathrm{s}^2$. The viscosity of the oil in SI unit is

JEE Main 2025 (Online) 3rd April Evening Shift
8

Consider a completely full cylindrical water tank of height 1.6 m and of cross-sectional area $0.5 \mathrm{~m}^2$. It has a small hole in its side at a height 90 cm from the bottom. Assume, the crosssectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is:

$$ \left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right) $$

JEE Main 2025 (Online) 3rd April Morning Shift
9
Two water drops each of radius ' $r$ ' coalesce to form a bigger drop. If ' $T$ ' is the surface tension, the surface energy released in this process is :
JEE Main 2025 (Online) 2nd April Evening Shift
10

The fractional compression $\left( \frac{\Delta V}{V} \right)$ of water at the depth of 2.5 km below the sea level is __________ %. Given, the Bulk modulus of water = $2 \times 10^9$ N m$^{-2}$, density of water = $10^3$ kg m$^{-3}$, acceleration due to gravity $g = 10$ m s$^{-2}$.

JEE Main 2025 (Online) 29th January Morning Shift
11

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water?

(Given: density of water = 1000 kg m-3)

JEE Main 2025 (Online) 28th January Evening Shift
12

In the experiment for measurement of viscosity ' $\eta$ ' of given liquid with a ball having radius $R$, consider following statements.

A. Graph between terminal velocity V and R will be a parabola.

B. The terminal velocities of different diameter balls are constant for a given liquid.

C. Measurement of terminal velocity is dependent on the temperature.

D. This experiment can be utilized to assess the density of a given liquid.

E. If balls are dropped with some initial speed, the value of $\eta$ will change.

Choose the correct answer from the options given below:

JEE Main 2025 (Online) 28th January Morning Shift
13

Consider following statements:

A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid.

B. As the temperature of liquid rises, the coefficient of viscosity increases.

C. As the temperature of gas increases, the coefficient of viscosity increases

D. The onset of turbulence is determined by Reynold's number.

E. In a steady flow two stream lines never intersect.

Choose the correct answer from the options given below:

JEE Main 2025 (Online) 28th January Morning Shift
14
An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density $1000 \mathrm{~kg} / \mathrm{m}^3$. If the pressure inside the bubble is $2100 \mathrm{~N} / \mathrm{m}^2$ greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use $g=10 \mathrm{~m} / \mathrm{s}^2$ )
JEE Main 2025 (Online) 24th January Morning Shift
15

The amount of work done to break a big water drop of radius ' $R$ ' into 27 small drops of equal radius is 10 J . The work done required to break the same big drop into 64 small drops of equal radius will be

JEE Main 2025 (Online) 24th January Morning Shift
16

A massless spring gets elongated by amount $x_1$ under a tension of 5 N . Its elongation is $x_2$ under the tension of 7 N . For the elongation of $\left(5 x_1-2 x_2\right)$, the tension in the spring will be,

JEE Main 2025 (Online) 23rd January Evening Shift
17

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$. The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to

JEE Main 2025 (Online) 23rd January Evening Shift
18

Given below are two statements:

Statement I: The hot water flows faster than cold water

Statement II: Soap water has higher surface tension as compared to fresh water. In the light above statements, choose the correct answer from the options given below

JEE Main 2025 (Online) 23rd January Morning Shift
19

JEE Main 2025 (Online) 22nd January Evening Shift Physics - Properties of Matter Question 27 English

A tube of length $L$ is shown in the figure. The radius of cross section at the point $(1)$ is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is $2 \mathrm{~m} / \mathrm{s}$, then velocity of water leaving the point (2) will be

JEE Main 2025 (Online) 22nd January Evening Shift
20

A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)

JEE Main 2025 (Online) 22nd January Evening Shift
21

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

JEE Main 2024 (Online) 9th April Evening Shift
22

A spherical ball of radius $$1 \times 10^{-4} \mathrm{~m}$$ and density $$10^5 \mathrm{~kg} / \mathrm{m}^3$$ falls freely under gravity through a distance $$h$$ before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of $$h$$ is approximately:

(The coefficient of viscosity of water is $$9.8 \times 10^{-6} \mathrm{~N} \mathrm{~s} / \mathrm{m}^2$$)

JEE Main 2024 (Online) 9th April Evening Shift
23

A sphere of relative density $$\sigma$$ and diameter $$D$$ has concentric cavity of diameter $$d$$. The ratio of $$\frac{D}{d}$$, if it just floats on water in a tank is :

JEE Main 2024 (Online) 9th April Morning Shift
24

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil = 0.8, specific gravity of ice = 0.9):

JEE Main 2024 (Online) 8th April Evening Shift Physics - Properties of Matter Question 44 English

JEE Main 2024 (Online) 8th April Evening Shift
25

Young's modulus is determined by the equation given by $$\mathrm{Y}=49000 \frac{\mathrm{m}}{\mathrm{l}} \frac{\mathrm{dyne}}{\mathrm{cm}^2}$$ where $$M$$ is the mass and $$l$$ is the extension of wire used in the experiment. Now error in Young modules $$(Y)$$ is estimated by taking data from $$M-l$$ plot in graph paper. The smallest scale divisions are $$5 \mathrm{~g}$$ and $$0.02 \mathrm{~cm}$$ along load axis and extension axis respectively. If the value of $M$ and $l$ are $$500 \mathrm{~g}$$ and $$2 \mathrm{~cm}$$ respectively then percentage error of $$Y$$ is :

JEE Main 2024 (Online) 8th April Morning Shift
26

Correct Bernoulli's equation is (symbols have their usual meaning) :

JEE Main 2024 (Online) 8th April Morning Shift
27

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $$\mathrm{R}=$$ Radius of bubble, $$\mathrm{S}=$$ Surface tension of bubble)

JEE Main 2024 (Online) 6th April Evening Shift
28

A small ball of mass $$m$$ and density $$\rho$$ is dropped in a viscous liquid of density $$\rho_0$$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

JEE Main 2024 (Online) 6th April Morning Shift
29

Match List I with List II :

LIST I
LIST II
A. A force that restores an elastic body of unit area to its original state I. Bulk modulus
B. Two equal and opposite forces parallel to opposite faces II. Young's modulus
C. Forces perpendicular everywhere to the surface per unit area same everywhere III. Stress
D. Two equal and opposite forces perpendicular to opposite faces Choose the correct answer from the options given below : IV. Shear modulus

Choose the correct answer from the options given below :

JEE Main 2024 (Online) 5th April Evening Shift
30

Given below are two statements :

Statement I : When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be $$0^{\circ}$$.

Statement II : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.

In the light of the above statement, choose the correct answer from the options given below.

JEE Main 2024 (Online) 5th April Morning Shift
31

Given below are two statements :

Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.

Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.

In the light of the above statements, choose the correct answer from the options given below :

JEE Main 2024 (Online) 4th April Evening Shift
32

Given below are two statements :

Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $$\mathrm{P}_1-\mathrm{P}_2=\rho g\left(\mathrm{~h}_2-\mathrm{h}_1\right)$$.

Statement II : In ventury tube shown $$2 \mathrm{gh}=v_1^2-v_2^2$$

JEE Main 2024 (Online) 4th April Morning Shift Physics - Properties of Matter Question 48 English

In the light of the above statements, choose the most appropriate answer from the options given below.

JEE Main 2024 (Online) 4th April Morning Shift
33
A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :
JEE Main 2024 (Online) 1st February Evening Shift
34
With rise in temperature, the Young's modulus of elasticity :
JEE Main 2024 (Online) 1st February Morning Shift
35

A small spherical ball of radius $$r$$, falling through a viscous medium of negligible density has terminal velocity '$$v$$'. Another ball of the same mass but of radius $$2 r$$, falling through the same viscous medium will have terminal velocity:

JEE Main 2024 (Online) 31st January Evening Shift
36

A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?

JEE Main 2024 (Online) 31st January Morning Shift
37

Young's modules of material of a wire of length '$$L$$' and cross-sectional area $$A$$ is $$Y$$. If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be :

JEE Main 2024 (Online) 30th January Morning Shift
38

A small liquid drop of radius $$R$$ is divided into 27 identical liquid drops. If the surface tension is $$T$$, then the work done in the process will be:

JEE Main 2024 (Online) 29th January Evening Shift
39

A wire of length $$L$$ and radius $$r$$ is clamped at one end. If its other end is pulled by a force $$F$$, its length increases by $$l$$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

JEE Main 2024 (Online) 29th January Evening Shift
40

Given below are two statements:

Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.

Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.

In the light of the above statements, choose the most appropriate from the options given below

JEE Main 2024 (Online) 29th January Morning Shift
41

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity.

Reason (R) : The restoring force depends upon the bonded inter atomic and inter molecular force of solid.

In the light of the above statements, choose the correct answer from the options given below :

JEE Main 2024 (Online) 27th January Evening Shift
42

Given below are two statements :

Statement (I) :Viscosity of gases is greater than that of liquids.

Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities.

In the light of the above statements, choose the most appropriate answer from the options given below :

JEE Main 2024 (Online) 27th January Morning Shift
43
A wire of length ' $L$ ' and radius ' $r$ ' is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$, its length increases by ' $l$ '. Another wire of same material of length ' $2 \mathrm{~L}$ ' and radius ' $2 r$ ' is pulled by a force ' $2 f$ '. Then the increase in its length will be :
JEE Main 2023 (Online) 15th April Morning Shift
44

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$

Assertion A : A spherical body of radius $$(5 \pm 0.1) \mathrm{mm}$$ having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is $$4 \%$$.

Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.

In the light of the above statements, choose the correct answer from the options given below

JEE Main 2023 (Online) 13th April Evening Shift
45

JEE Main 2023 (Online) 13th April Morning Shift Physics - Properties of Matter Question 93 English

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at $$\mathrm{A}$$ is $$1.5 \mathrm{~cm}^{2}$$, and $$\mathrm{B}$$ is $$25 \mathrm{~mm}^{2}$$, if the speed of liquid at $$\mathrm{B}$$ is $$60 \mathrm{~cm} / \mathrm{s}$$ then $$\left(\mathrm{P}_{\mathrm{A}}-\mathrm{P}_{\mathrm{B}}\right)$$ is :

(Given $$\mathrm{P}_{\mathrm{A}}$$ and $$\mathrm{P}_{\mathrm{B}}$$ are liquid pressures at $$\mathrm{A}$$ and $$\mathrm{B}$$% points.

density $$\rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$$

$$\mathrm{A}$$ and $$\mathrm{B}$$ are on the axis of tube

JEE Main 2023 (Online) 13th April Morning Shift
46

Under isothermal condition, the pressure of a gas is given by $$\mathrm{P}=a \mathrm{~V}^{-3}$$, where $$a$$ is a constant and $$\mathrm{V}$$ is the volume of the gas. The bulk modulus at constant temperature is equal to

JEE Main 2023 (Online) 13th April Morning Shift
47

A body cools from $$80^{\circ} \mathrm{C}$$ to $$60^{\circ} \mathrm{C}$$ in 5 minutes. The temperature of the surrounding is $$20^{\circ} \mathrm{C}$$. The time it takes to cool from $$60^{\circ} \mathrm{C}$$ to $$40^{\circ} \mathrm{C}$$ is :

JEE Main 2023 (Online) 12th April Morning Shift
48

Eight equal drops of water are falling through air with a steady speed of $$10 \mathrm{~cm} / \mathrm{s}$$. If the drops coalesce, the new velocity is:-

JEE Main 2023 (Online) 11th April Evening Shift
49

Young's moduli of the material of wires A and B are in the ratio of $$1: 4$$, while its area of cross sections are in the ratio of $$1: 3$$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires $$\mathrm{A}$$ and $$\mathrm{B}$$ will be in the ratio of

[Assume length of wires A and B are same]

JEE Main 2023 (Online) 10th April Evening Shift
50

Given below are two statements:

Statement I : Pressure in a reservoir of water is same at all points at the same level of water.

Statement II : The pressure applied to enclosed water is transmitted in all directions equally.

In the light of the above statements, choose the correct answer from the options given below:

JEE Main 2023 (Online) 10th April Morning Shift
51

A hydraulic automobile lift is designed to lift vehicles of mass $$5000 \mathrm{~kg}$$. The area of cross section of the cylinder carrying the load is $$250 \mathrm{~cm}^{2}$$. The maximum pressure the smaller piston would have to bear is $$\left[\right.$$ Assume $$\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right]$$

JEE Main 2023 (Online) 8th April Evening Shift
52

An air bubble of volume $$1 \mathrm{~cm}^{3}$$ rises from the bottom of a lake $$40 \mathrm{~m}$$ deep to the surface at a temperature of $$12^{\circ} \mathrm{C}$$. The atmospheric pressure is $$1 \times 10^{5} \mathrm{~Pa}$$ the density of water is $$1000 \mathrm{~kg} / \mathrm{m}^{3}$$ and $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$$. There is no difference of the temperature of water at the depth of $$40 \mathrm{~m}$$ and on the surface. The volume of air bubble when it reaches the surface will be:

JEE Main 2023 (Online) 8th April Morning Shift
53

An aluminium rod with Young's modulus $$Y=7.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$$ undergoes elastic strain of $$0.04 \%$$. The energy per unit volume stored in the rod in SI unit is:

JEE Main 2023 (Online) 8th April Morning Shift
54

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$

Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed.

Reason R: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.

In the light of the above statements, choose the most appropriate answer from the options given below

JEE Main 2023 (Online) 6th April Evening Shift
55

A small ball of mass $$\mathrm{M}$$ and density $$\rho$$ is dropped in a viscous liquid of density $$\rho_{0}$$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?

JEE Main 2023 (Online) 6th April Morning Shift
56

The Young's modulus of a steel wire of length $$6 \mathrm{~m}$$ and cross-sectional area $$3 \mathrm{~mm}^{2}$$, is $$2 \times 10^{11}~\mathrm{N} / \mathrm{m}^{2}$$. The wire is suspended from its support on a given planet. A block of mass $$4 \mathrm{~kg}$$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $$\frac{1}{4}$$ of its value on the earth. The elongation of wire is (Take $$g$$ on the earth $$=10 \mathrm{~m} / \mathrm{s}^{2}$$) :

JEE Main 2023 (Online) 1st February Evening Shift
57

A mercury drop of radius $$10^{-3}~\mathrm{m}$$ is broken into 125 equal size droplets. Surface tension of mercury is $$0.45~\mathrm{Nm}^{-1}$$. The gain in surface energy is :

JEE Main 2023 (Online) 1st February Morning Shift
58
For a solid rod, the Young's modulus of elasticity is $3.2 \times 10^{11} \mathrm{Nm}^{-2}$ and density is $8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$. The velocity of longitudinal wave in the rod will be.
JEE Main 2023 (Online) 31st January Evening Shift
59
Under the same load, wire A having length $5.0 \mathrm{~m}$ and cross section $2.5 \times 10^{-5} \mathrm{~m}^{2}$ stretches uniformly by the same amount as another wire B of length $6.0 \mathrm{~m}$ and a cross section of $3.0 \times 10^{-5}$ $\mathrm{m}^{2}$ stretches. The ratio of the Young's modulus of wire A to that of wire $B$ will be :
JEE Main 2023 (Online) 31st January Evening Shift
60

If 1000 droplets of water of surface tension $$0.07 \mathrm{~N} / \mathrm{m}$$, having same radius $$1 \mathrm{~mm}$$ each, combine to from a single drop. In the process the released surface energy is :-

$$\left( {\mathrm{Take}\,\pi = {{22} \over 7}} \right)$$

JEE Main 2023 (Online) 31st January Morning Shift
61
A force is applied to a steel wire 'A', rigidly clamped at one end. As a result elongation in the wire is $0.2 \mathrm{~mm}$. If same force is applied to another steel wire ' $\mathrm{B}$ ' of double the length and a diameter $2.4$ times that of the wire ' $\mathrm{A}$ ', the elongation in the wire ' $\mathrm{B}$ ' will be (wires having uniform circular cross sections)
JEE Main 2023 (Online) 30th January Evening Shift
62

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, $$5 \mathrm{~cm}$$. If the tube is dipped in a similar manner in another liquid $$\mathrm{B}$$ of surface tension and density double the values of liquid $$\mathrm{A}$$, the height of liquid column raised in liquid $$\mathrm{B}$$ would be __________ m.

JEE Main 2023 (Online) 30th January Morning Shift
63

Choose the correct relationship between Poisson ratio $$(\sigma)$$, bulk modulus (K) and modulus of rigidity $$(\eta)$$ of a given solid object :

JEE Main 2023 (Online) 30th January Morning Shift
64

A fully loaded boeing aircraft has a mass of $$5.4\times10^5$$ kg. Its total wing area is 500 m$$^2$$. It is in level flight with a speed of 1080 km/h. If the density of air $$\rho$$ is 1.2 kg m$$^{-3}$$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. ($$\mathrm{g=10~m/s^2}$$)

JEE Main 2023 (Online) 29th January Evening Shift
65

Surface tension of a soap bubble is $$2.0 \times 10^{-2} \mathrm{Nm}^{-1}$$. Work done to increase the radius of soap bubble from $$3.5 \mathrm{~cm}$$ to $$7 \mathrm{~cm}$$ will be:

Take $$\left[\pi=\frac{22}{7}\right]$$

JEE Main 2023 (Online) 29th January Morning Shift
66

A bicycle tyre is filled with air having pressure of $$270 ~\mathrm{kPa}$$ at $$27^{\circ} \mathrm{C}$$. The approximate pressure of the air in the tyre when the temperature increases to $$36^{\circ} \mathrm{C}$$ is

JEE Main 2023 (Online) 29th January Morning Shift
67

Match List I with List II

List I List II
A. Surface tension I. $$\mathrm{kg~m^{-1}~s^{-1}}$$
B. Pressure II. $$\mathrm{kg~ms^{-1}}$$
C. Viscosity III. $$\mathrm{kg~m^{-1}~s^{-2}}$$
D. Impulse IV. $$\mathrm{kg~s^{-2}}$$

Choose the correct answer from the options given below :

JEE Main 2023 (Online) 25th January Morning Shift
68

A bowl filled with very hot soup cools from 98$$^\circ$$C to 86$$^\circ$$C in 2 minutes when the room temperature is 22$$^\circ$$C. How long it will take to cool from 75$$^\circ$$C to 69$$^\circ$$C?

JEE Main 2023 (Online) 25th January Morning Shift
69

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : Steel is used in the construction of buildings and bridges.

Reason R : Steel is more elastic and its elastic limit is high.

In the light of above statements, choose the most appropriate answer from the options given below

JEE Main 2023 (Online) 24th January Evening Shift
70

The frequency ($$\nu$$) of an oscillating liquid drop may depend upon radius ($$r$$) of the drop, density ($$\rho$$) of liquid and the surface tension (s) of the liquid as $$\nu=r^a\rho^b s^c$$. The values of a, b and c respectively are

JEE Main 2023 (Online) 24th January Evening Shift
71

A 100 m long wire having cross-sectional area $$\mathrm{6.25\times10^{-4}~m^2}$$ and Young's modulus is $$\mathrm{10^{10}~Nm^{-2}}$$ is subjected to a load of 250 N, then the elongation in the wire will be :

JEE Main 2023 (Online) 24th January Morning Shift
72

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): Clothes containing oil or grease stains cannot be cleaned by water wash.

Reason (R): Because the angle of contact between the oil/grease and water is obtuse.

In the light of the above statements, choose the correct answer from the option given below.

JEE Main 2022 (Online) 29th July Morning Shift
73

If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will :

JEE Main 2022 (Online) 29th July Morning Shift
74

A pressure-pump has a horizontal tube of cross sectional area $$10 \mathrm{~cm}^{2}$$ for the outflow of water at a speed of $$20 \mathrm{~m} / \mathrm{s}$$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is :

[given: density of water $$=1000 \mathrm{~kg} / \mathrm{m}^{3}$$]

JEE Main 2022 (Online) 28th July Evening Shift
75

Consider a cylindrical tank of radius $$1 \mathrm{~m}$$ is filled with water. The top surface of water is at $$15 \mathrm{~m}$$ from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of $$5 \mathrm{~m}$$ from the bottom. A force of $$5 \times 10^{5} \mathrm{~N}$$ is applied an the top surface of water using a piston. The speed of ifflux from the hole will be : (given atmospheric pressure $$\mathrm{P}_{\mathrm{A}}=1.01 \times 10^{5} \mathrm{~Pa}$$, density of water $$\rho_{\mathrm{W}}=1000 \mathrm{~kg} / \mathrm{m}^{3}$$ and gravitational acceleration $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$$ )

JEE Main 2022 (Online) 28th July Evening Shift Physics - Properties of Matter Question 132 English

JEE Main 2022 (Online) 28th July Evening Shift
76

A balloon has mass of $$10 \mathrm{~g}$$ in air. The air escapes from the balloon at a uniform rate with velocity $$4.5 \mathrm{~cm} / \mathrm{s}$$. If the balloon shrinks in $$5 \mathrm{~s}$$ completely. Then, the average force acting on that balloon will be (in dyne).

JEE Main 2022 (Online) 28th July Morning Shift
77

The force required to stretch a wire of cross-section $$1 \mathrm{~cm}^{2}$$ to double its length will be : (Given Yong's modulus of the wire $$=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$$)

JEE Main 2022 (Online) 28th July Morning Shift
78

A steel wire of length $$3.2 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{s}}=2.0 \times 10^{11} \,\mathrm{Nm}^{-2}\right)$$ and a copper wire of length $$4.4 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{c}}=1.1 \times 10^{11} \,\mathrm{Nm}^{-2}\right)$$, both of radius $$1.4 \mathrm{~mm}$$ are connected end to end. When stretched by a load, the net elongation is found to be $$1.4 \mathrm{~mm}$$. The load applied, in Newton, will be: $$\quad\left(\right.$$ Given $$\pi=\frac{22}{7}$$)

JEE Main 2022 (Online) 27th July Evening Shift
79

Two cylindrical vessels of equal cross-sectional area $$16 \mathrm{~cm}^{2}$$ contain water upto heights $$100 \mathrm{~cm}$$ and $$150 \mathrm{~cm}$$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take, density of water $$=10^{3} \mathrm{~kg} / \mathrm{m}^{3}$$ and $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$ ] :

JEE Main 2022 (Online) 27th July Morning Shift
80

The area of cross section of the rope used to lift a load by a crane is $$2.5 \times 10^{-4} \mathrm{~m}^{2}$$. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be :

(take $$g=10 \,m s^{-2}$$ )

JEE Main 2022 (Online) 26th July Evening Shift
81

A water drop of radius $$1 \mathrm{~cm}$$ is broken into 729 equal droplets. If surface tension of water is 75 dyne/ $$\mathrm{cm}$$, then the gain in surface energy upto first decimal place will be :

(Given $$\pi=3.14$$ )

JEE Main 2022 (Online) 26th July Morning Shift
82

A drop of liquid of density $$\rho$$ is floating half immersed in a liquid of density $${\sigma}$$ and surface tension $$7.5 \times 10^{-4}$$ Ncm$$-$$1. The radius of drop in $$\mathrm{cm}$$ will be :

(g = 10 ms$$-$$2)

JEE Main 2022 (Online) 25th July Evening Shift
83

An air bubble of negligible weight having radius r rises steadily through a solution of density $$\sigma$$ at speed v. The coefficient of viscosity of the solution is given by :

JEE Main 2022 (Online) 30th June Morning Shift
84

A wire of length L is hanging from a fixed support. The length changes to L1 and L2 when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to :

JEE Main 2022 (Online) 29th June Morning Shift
85

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs$$-$$1 and at a speed of 10 ms$$-$$1. Then, the initial acceleration of the block, in ms$$-$$2, will be :

JEE Main 2022 (Online) 29th June Morning Shift Physics - Properties of Matter Question 166 English

JEE Main 2022 (Online) 29th June Morning Shift
86

A water drop of radius 1 $$\mu$$m falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 $$\times$$ 10$$-$$5 Nsm$$-$$2 and its density is negligible as compared to that of water 106 gm$$-$$3. Terminal velocity of the water drop is :

(Take acceleration due to gravity = 10 ms$$-$$2)

JEE Main 2022 (Online) 28th June Evening Shift
87

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.

Reason R : Coefficient of viscosity = $${{Force} \over {Velocity\,gradient}}$$

Choose the correct answer from the options given below :

JEE Main 2022 (Online) 28th June Morning Shift
88

A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be :

JEE Main 2022 (Online) 28th June Morning Shift
89

When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

JEE Main 2022 (Online) 27th June Evening Shift
90

The velocity of a small ball of mass 'm' and density d1, when dropped in a container filled with glycerin, becomes constant after some time. If the density of glycerin is d2, then the viscous force acting on the ball, will be :

JEE Main 2022 (Online) 27th June Morning Shift
91

If p is the density and $$\eta$$ is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number Re is :

JEE Main 2022 (Online) 26th June Evening Shift
92

The terminal velocity (vt) of the spherical rain drop depends on the radius (r) of the spherical rain drop as :

JEE Main 2022 (Online) 25th June Morning Shift
93

Potential energy as a function of r is given by $$U = {A \over {{r^{10}}}} - {B \over {{r^5}}}$$, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

JEE Main 2022 (Online) 24th June Evening Shift
94

The bulk modulus of a liquid is 3 $$\times$$ 1010 Nm$$-$$2. The pressure required to reduce the volume of liquid by 2% is :

JEE Main 2022 (Online) 24th June Morning Shift
95
Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $$\times$$ 103 kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 $$\times$$ 1011 Pa, g = 9.8 m/s2]
JEE Main 2021 (Online) 31st August Evening Shift
96
A uniform heavy rod of weight 10 kg ms$$-$$2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 $$\times$$ 1011 Nm$$-$$2. Neglecting the lateral contraction, find the elongation of rod due to its own weight.
JEE Main 2021 (Online) 31st August Morning Shift
97
In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 $$\times$$ 10$$-$$5 m and density 1.2 $$\times$$ 103 kgm$$-$$3 ? Take viscosity of liquid = 1.8 $$\times$$ 10$$-$$5 Nsm$$-$$2. (Neglect buoyancy due to air).
JEE Main 2021 (Online) 27th August Morning Shift
98
Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $${{24} \over \pi } \times {10^2}$$ Nm-2. What is the minimum radius of the wire ? (Take g = 10 ms-2)

JEE Main 2021 (Online) 26th August Evening Shift Physics - Properties of Matter Question 173 English
JEE Main 2021 (Online) 26th August Evening Shift
99
Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7.3 $$\times$$ 10$$-$$2 Nm$$-$$1, angle of contact = 0, g = 10 ms2 and density of water = 1.0 $$\times$$ 103 kg m$$-$$3]
JEE Main 2021 (Online) 26th August Morning Shift
100
A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is :

[Density of water fw = 1000 kg m$$-$$3 and Density of air fa = 1.2 kg m$$-$$3, g = 10 m/s2, Coefficient of viscosity of air = 1.8 $$\times$$ 10$$-$$5 Nsm$$-$$2]
JEE Main 2021 (Online) 27th July Evening Shift
101
A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a < < A) :

JEE Main 2021 (Online) 27th July Morning Shift Physics - Properties of Matter Question 180 English
JEE Main 2021 (Online) 27th July Morning Shift
102
A body takes 4 min. to cool from 61$$^\circ$$ C to 59$$^\circ$$ C. If the temperature of the surroundings is 30$$^\circ$$ C, the time taken by the body to cool from 51$$^\circ$$ C to 49$$^\circ$$ C is :
JEE Main 2021 (Online) 27th July Morning Shift
103
Two spherical soap bubbles of radii r1 and r2 in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to :
JEE Main 2021 (Online) 25th July Evening Shift
104
Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y1 and Y2. The combination behaves as a single wire then its Young's modulus is :
JEE Main 2021 (Online) 25th July Morning Shift
105
The length of a metal wire is l1, when the tension in it is T1 and is l2 when the tension is T2. The natural length of the wire is :
JEE Main 2021 (Online) 20th July Evening Shift
106
Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy before and after the change is :
JEE Main 2021 (Online) 20th July Evening Shift
107
The value of tension in a long thin metal wire has been changed from T1 to T2. The lengths of the metal wire at two different values of tension T1 and T2 are l1 and l2 respectively. The actual length of the metal wire is :
JEE Main 2021 (Online) 20th July Morning Shift
108
An object is located at 2 km beneath the surface of the water. If the fractional compression $${{\Delta V} \over V}$$ is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given : density of water is 1000 kgm$$-$$3 and g = 9.8 ms$$-$$2]
JEE Main 2021 (Online) 17th March Evening Shift
109
When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface is :
JEE Main 2021 (Online) 17th March Morning Shift
110
What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water are 0.5 cm and 10$$-$$3 Pa s, respectively. (Density of water : 103 kg/m3)
JEE Main 2021 (Online) 16th March Evening Shift
111
The pressure acting on a submarine is 3 $$\times$$ 105 Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be :

(Assume that atmospheric pressure is 1 $$\times$$ 105 Pa density of water is 103 kg m$$-$$3, g = 10 ms$$-$$2)
JEE Main 2021 (Online) 16th March Morning Shift
112
The length of metallic wire is l1 when tension in it is T1. It is l2 when the tension is T2. The original length of the wire will be :
JEE Main 2021 (Online) 26th February Evening Shift
113
A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be :
JEE Main 2021 (Online) 26th February Morning Shift
114
The normal density of a material is $$\rho$$ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :
JEE Main 2021 (Online) 26th February Morning Shift
115
If Y, K and $$\eta $$ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.
JEE Main 2021 (Online) 24th February Morning Shift
116
A fluid is flowing through a horizontal pipe of varying cross-section, with
speed v ms–1 at a point where the pressure is P pascal. At another point where pressure is $${P \over 2}$$ Pascal its speed is V ms–1. If the density of the fluid is $$\rho $$ kg m–3 and the flow is streamline, then V is equal to :
JEE Main 2020 (Online) 6th September Evening Slot
117
An object of mass m is suspended at the end of a massless wire of length L and area of crosssection A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is :
JEE Main 2020 (Online) 6th September Morning Slot
118
In an experiment to verify Stokes law, a small spherical ball of radius r and density $$\rho $$ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to :
(ignore viscosity of air)
JEE Main 2020 (Online) 5th September Evening Slot
119
A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is $${{27} \over 8}$$ w.r.t water, the value of r is :
JEE Main 2020 (Online) 5th September Morning Slot
120
Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x1 and in the other, x2 . When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is:
JEE Main 2020 (Online) 4th September Evening Slot
121
A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the length of the side of the cube is close to :
(Given bulk modulus of metal, B = 8 $$ \times $$ 1010 Pa)
JEE Main 2020 (Online) 4th September Evening Slot
122
A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s–2. The density of water is 1 gm cm–3 and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980 cm/s2).
JEE Main 2020 (Online) 4th September Morning Slot
123
A metallic sphere cools from 50oC to 40o in 300 s. If atmospheric temperature around is 20oC, then the sphere’s temperature after the next 5 minutes will be close to :
JEE Main 2020 (Online) 3rd September Evening Slot
124
Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :
JEE Main 2020 (Online) 3rd September Morning Slot
125
A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 Nm–1, density = 667 kg m–3) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60o with one another. Then h is close to (g = 10 ms–2)
JEE Main 2020 (Online) 2nd September Evening Slot
126
A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is $$\omega $$ rad s–1. The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be : JEE Main 2020 (Online) 2nd September Morning Slot Physics - Properties of Matter Question 212 English
JEE Main 2020 (Online) 2nd September Morning Slot
127
A small spherical droplet of density d is floating exactly half immersed in a liquid of density $$\rho $$ and surface tension T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet) :
JEE Main 2020 (Online) 9th January Evening Slot
128
Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:
JEE Main 2020 (Online) 9th January Evening Slot
129
Water flows in a horizontal tube (see figure).
The pressure of water changes by 700 Nm–2
between A and B where the area of cross section
are 40 cm2 and 20 cm2, respectively. Find the
rate of flow of water through the tube.
(density of water = 1000 kgm–3) JEE Main 2020 (Online) 9th January Morning Slot Physics - Properties of Matter Question 215 English
JEE Main 2020 (Online) 9th January Morning Slot
130
Two liquids of densities $${\rho _1}$$ an $${\rho _2}$$ ($${\rho _2}$$ = 2$${\rho _1}$$) are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing) JEE Main 2020 (Online) 8th January Evening Slot Physics - Properties of Matter Question 216 English
JEE Main 2020 (Online) 8th January Evening Slot
131
Consider a solid sphere of radius R and mass density
$$\rho \left( r \right) = {\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right)$$ , $$0 < r \le R$$
The minimum density of a liquid in which it will float is :
JEE Main 2020 (Online) 8th January Morning Slot
132
A leak proof cylinder of length 1m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0°C such that its height above the water surface is 20 cm. When the temperature of water is increased to 4°C, the height of the cylinder above the water surface becomes 21 cm. The density of water at T = 4°C, relative to the density at T = 0°C is close to :
JEE Main 2020 (Online) 8th January Morning Slot
133
An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is :
JEE Main 2020 (Online) 7th January Evening Slot
134
A solid sphere, of radius R acquires a terminal velocity v1 when falling (due to gravity) through a viscous fluid having a coefficient of viscosity . The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v2, when falling through the same fluid, the ratio (v1/v2) equals :
JEE Main 2019 (Online) 12th April Evening Slot
135
The number density of molecules of a gas depends on their distance r from the origin as, $$n\left( r \right) = {n_0}{e^{ - \alpha {r^4}}}$$. Then the total number of molecules is proportional to :
JEE Main 2019 (Online) 12th April Evening Slot
136
A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to :
JEE Main 2019 (Online) 12th April Evening Slot
137
Water from a tap emerges vertically downwards with an initial speed of 1.0 ms–1 . The cross-sectional area of the tap is 10–4 m2. Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross-sectional area of the stream, 0.15 m below the tap would be : (Take g = 10 ms–2)
JEE Main 2019 (Online) 10th April Evening Slot
138
A submarine experiences a pressure of 5.05 × 106 Pa at a depth of d1 in a sea. When it goes further to a depth of d2, it experiences a pressure of 8.08 × 106 Pa. Then d2 –d1 is approximately (density of water = 103 kg/m3 and acceleration due to gravity = 10 ms–2 ) :
JEE Main 2019 (Online) 10th April Evening Slot
139
In an experiment, brass and steel wires of length 1 m each with areas of cross section 1mm2 are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is, [Given, the Young's Modulus for steel and brass are, respectively, 120 × 109 N/m2 and 60 × 109 N/m2]
JEE Main 2019 (Online) 10th April Evening Slot
140
A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? [Take, density of water = 103 kg/m3]
JEE Main 2019 (Online) 10th April Evening Slot
141
The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit?
JEE Main 2019 (Online) 10th April Evening Slot
142
The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of thier densities is 13.6. Their contact angles, with glass, are close to 135° and 0°, respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius r1, while water rises by the same amount h in a capillary tube of radius r2. The ratio, (r1/r2), is then close to :
JEE Main 2019 (Online) 10th April Morning Slot
143
A wooden block floating in a bucket of water has 4/5 of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is :-
JEE Main 2019 (Online) 9th April Evening Slot
144
If 'M' is the mass of water that rises in a capillary tube of radius 'r', then mass of water which will rise in a capillary tube of radius '2r' is :
JEE Main 2019 (Online) 9th April Morning Slot
145
A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is 1/16 th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is :
JEE Main 2019 (Online) 9th April Morning Slot
146
Young's moduli of two wires A and B are in the ratio 7 : 4. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of R is close to :-
JEE Main 2019 (Online) 8th April Evening Slot
147
A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms–1. Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to:
JEE Main 2019 (Online) 8th April Morning Slot
148
Water from a pipe is coming at a rate of 100 litres per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water = 1000 kg/m3, coefficient of viscosity of water = 1mPas)
JEE Main 2019 (Online) 8th April Morning Slot
149
A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1 p ms–2, what will be the tensile stress that would be developed in the wire ?
JEE Main 2019 (Online) 8th April Morning Slot
150
A load of mass M kg is suspended from a steel wire of length 2m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8.

The new value of increase in length of the steel wire is:
JEE Main 2019 (Online) 12th January Evening Slot
151
A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by :
JEE Main 2019 (Online) 12th January Evening Slot
152
A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be :
JEE Main 2019 (Online) 12th January Evening Slot
153
A liquid of density $$\rho $$ is coming out of a hose pipe of radius a with horizontal speed $$\upsilon $$ and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be :
JEE Main 2019 (Online) 11th January Morning Slot
154
Water flows into a large tank with flat bottom at the rate of 10–4m3s–1. Water is also leaking out of a hole ofarea 1 cm2 at its bottom. If the height of the water in the tank remains steady, then this height is -
JEE Main 2019 (Online) 10th January Morning Slot
155
The top of a water tank is open to air and its water level is mainted. It is giving out 0.74 m3 water per minute through a circular opening of 2 cm radius in its wall. The depth of the center of the opening from the level of water in the tank is close to :
JEE Main 2019 (Online) 9th January Evening Slot
156
A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P2 be the pressure inside the inner bubble and P0, the pressure outside the outer bubble. Radius of another bubble with pressure difference P2 $$-$$ P0 between its inside and outside would be :
JEE Main 2018 (Online) 16th April Morning Slot
157
A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $$\left( {{dr \over r}} \right)$$ is:
JEE Main 2018 (Offline)
158
As shown in the figure, forces of 105 N each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm, shifting the upper face parallel to itself by 0.5 cm. If the side of another cube of the same material is 20 cm, then under similar conditions as above, the displacement will be :
JEE Main 2018 (Online) 15th April Evening Slot Physics - Properties of Matter Question 250 English
JEE Main 2018 (Online) 15th April Evening Slot
159
When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes $${{5r} \over 4}.$$ Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature) :
JEE Main 2018 (Online) 15th April Evening Slot
160
A body takes 10 minutes to cool from 60oC to 50oC. The tempertature of surroundings is constant at 25oC. Then, the temperature of the body after next 10 minutes will be approximately :
JEE Main 2018 (Online) 15th April Evening Slot
161
A thin uniform tube is bent into a circle of radius $$r$$ in the vertical plane. Equal volumes of two immiscible liquids, whose densities are $${\rho _1}$$ and $${\rho _2}$$ $$\left( {{\rho _1} > {\rho _2}} \right),$$ fill half the circle. The angle $$\theta $$ between the radius vector passing through the common interface and the vertical is :
JEE Main 2018 (Online) 15th April Morning Slot
162
Two tubes of radii r1 and r2, and lengths l1 and l2 , respectively, are connected in series and a liquid flows through each of them in stream line conditions. P1 and P2 are pressure differences across the two tubes.

If P2 is 4P1 and l2 is $${{{1_1}} \over 4}$$, then the radius r2 will be equal to :
JEE Main 2017 (Online) 9th April Morning Slot
163
A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of :
JEE Main 2017 (Offline)
164
A bottle has an opening of radius a and length b. A cork of length b and radius (a + $$\Delta $$a) where ($$\Delta $$a < < a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is $$\mu $$ then the force needed to push the cork into the bottle is :

JEE Main 2016 (Online) 10th April Morning Slot Physics - Properties of Matter Question 242 English
JEE Main 2016 (Online) 10th April Morning Slot
165
A thin 1 m long rod has a radius of 5 mm. A force of 50 $$\pi $$kN is applied at one end to determine its Young’s modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false ?
JEE Main 2016 (Online) 10th April Morning Slot
166
JEE Main 2016 (Online) 9th April Morning Slot Physics - Properties of Matter Question 244 English
Consider a water jar of radius R that has water filled up to height H and is kept on astand of height h (see figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then :
JEE Main 2016 (Online) 9th April Morning Slot
167
Which of the following option correctly describes the variation of the speed v and acceleration ‘a’ of a point mass falling vertically in a viscous medium that applies a force F = − kv, where ‘k’ is a constant, on the body ? (Graphs are schematic and not drawn to scale)
JEE Main 2016 (Online) 9th April Morning Slot
168
A uniformly tapering conical wire is made from a material of Young’s modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3 R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal :
JEE Main 2016 (Online) 9th April Morning Slot
169
On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius $$R$$ and making a circular contact of radius $$r$$ with the bottom $$R$$ and making a circular contact of radius $$r$$ with the bottom of the vessel. If $$r < < R$$ and the surface tension of water is $$T,$$ value of $$r$$ just before bubbles detach is: (density of water is $${\rho _w}$$) JEE Main 2014 (Offline) Physics - Properties of Matter Question 258 English
JEE Main 2014 (Offline)
170
There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $${d_1}$$ and $${d_2}$$ are filled in the tube. Each liquid subtends $${90^ \circ }$$ angle at center. Radius joining their interface makes an angle $$\alpha $$ with vertical. Radio $${{{d_1}} \over {{d_2}}}$$ is : JEE Main 2014 (Offline) Physics - Properties of Matter Question 255 English
JEE Main 2014 (Offline)
171
The pressure that has to be applied to the ends of a steel wire of length $$10$$ $$cm$$ to keep its length constant when its temperature is raised by $${100^ \circ }C$$ is: (For steel Young's modulus is $$2 \times {10^{11}}\,\,N{m^{ - 2}}$$ and coefficient of thermal expansion is $$1.1 \times {10^{ - 5}}\,{K^{ - 1}}$$ )
JEE Main 2014 (Offline)
172
An open glass tube is immersed in mercury in such a way that a length of $$8$$ $$cm$$ extends above the mercury level. The open end of the tube is then closed and scaled and the tube is raised vertically up by additional $$46$$ $$cm$$. What will be length of the air column above mercury in the tube now? (Atmospheric pressure $$=76$$ $$cm$$ of $$Hg$$)
JEE Main 2014 (Offline)
173
If a piece of metal is heated to temperature $$\theta $$ and then allowed to cool in a room which is at temperature $${\theta _0},$$ the graph between the temperature $$T$$ of the metal and time $$t$$ will be closest to
JEE Main 2013 (Offline)
174
A uniform cylinder of length $$L$$ and mass $$M$$ having cross-sectional area $$A$$ is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density $$\sigma $$ at equilibrium position. The extension $${x_0}$$ of the spring when it is in equilibrium is:
JEE Main 2013 (Offline)
175
A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $$1.5 \times {10^{ - 2}}\,\,N$$ (see figure). The length of the slider is $$30$$ $$cm$$ and its weight negligible. The surface tension of the liquid film is AIEEE 2012 Physics - Properties of Matter Question 260 English
AIEEE 2012
176
A liquid in a beaker has temperature $$\theta \left( t \right)$$ at time $$t$$ and $${\theta _0}$$ is temperature of surroundings, then according to Newton's law of cooling the correct graph between $${\log _e}\left( {\theta - {\theta _0}} \right)$$ and $$t$$ is :
AIEEE 2012
177
Water is flowing continuously from a tap having an internal diameter $$8 \times {10^{ - 3}}\,\,m.$$ The water velocity as it leaves the tap is $$0.4\,\,m{s^{ - 1}}$$ . The diameter of the water stream at a distance $$2 \times {10^{ - 1}}\,\,m$$ below the tap is close to :
AIEEE 2011
178
Work done in increasing the size of a soap bubble from a radius of $$3$$ $$cm$$ to $$5$$ $$cm$$ is nearly (Surface tension of soap solution $$ = 0.03N{m^{ - 1}},$$
AIEEE 2011
179
A ball is made of a material of density $$\rho $$ where $${\rho _{oil}}\, < \rho < {\rho _{water}}$$ with $${\rho _{oil}}$$ and $${\rho _{water}}$$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?
AIEEE 2010
180
Two wires are made of the same material and have the same volume. However wire $$1$$ has cross-sectional area $$A$$ and wire $$2$$ has cross-sectional area $$3A.$$ If the length of wire $$1$$ increases by $$\Delta x$$ on applying force $$F,$$ how much force is needed to stretch wire $$2$$ by the same amount?
AIEEE 2009
181
A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?
AIEEE 2008
182
A jar is filled with two non-mixing liquids $$1$$ and $$2$$ having densities $${\rho _1}$$ and $${\rho _2}$$ respectively. A solid ball, made of a material of density $${\rho _3}$$, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $${\rho _1}$$ , $${\rho _1}$$ and $${\rho _3}$$ ? AIEEE 2008 Physics - Properties of Matter Question 262 English
AIEEE 2008
183
A spherical solid ball of volume $$V$$ is made of a material of density $${\rho _1}$$. It is falling through a liquid of density $${\rho _2}\left( {{\rho _2} < {\rho _1}} \right)$$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $$v,$$ i.e., $${F_{viscous}} = - k{v^2}\left( {k > 0} \right).$$ The terminal speed of the ball is
AIEEE 2008
184
If the terminal speed of a sphere of gold (density $$ = 19.5\,\,kg/{m^3}$$) is $$0.2$$ $$m/s$$ in a viscous liquid (density $$ = 1.5\,\,kg/{m^3}$$, find the terminal speed of a sphere of silver (density $$ = 10.5\,\,kg/{m^3}$$) of the same size in the same liquid
AIEEE 2006
185
A wire elongates by $$l$$ $$mm$$ when a LOAD $$W$$ is hanged from it. If the wire goes over a pulley and two weights $$W$$ each are hung at the two ends, the elongation of the wire will be (in $$mm$$)
AIEEE 2006
186
If $$S$$ is stress and $$Y$$ is young's modulus of material of a wire, the energy stored in the wire per unit volume is
AIEEE 2005
187
A $$20$$ $$cm$$ long capillary tube is dipped in water. The water rises up to $$8$$ $$cm.$$ If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be
AIEEE 2005
188
A wire fixed at the upper end stretches by length $$l$$ by applying a force $$F.$$ The work done in stretching is
AIEEE 2004
189
Spherical balls of radius $$R$$ are falling in a viscous fluid of viscosity $$\eta $$ with a velocity $$v.$$ The retarding viscous force acting on the spherical ball is
AIEEE 2004
190
If two soap bubbles of different radii are connected by a tube
AIEEE 2004
191
According to Newton's law of cooling, the rate of cooling of a body is proportional to $${\left( {\Delta \theta } \right)^n},$$ where $${\Delta \theta }$$ is the difference of the temperature of the body and the surrounding, and $$n$$ is equal to :
AIEEE 2003
192
A cylinder of height $$20$$ $$m$$ is completely filled with water. The velocity of efflux of water (in $$m{s^{ - 1}}$$) through a small hole on the side wall of the cylinder near its bottom is
AIEEE 2002

Numerical

1

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to a change of volume of 0.8 cm3. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was _______ litre.

(Take 1 atm = 105 Pa)

JEE Main 2025 (Online) 8th April Evening Shift
2

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of a uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water.

(Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is 1 gm/cm3.)

The unknown mass is _____ kg.

JEE Main 2025 (Online) 8th April Evening Shift
3

Two slabs with square cross section of different materials $(1,2)$ with equal sides $(l)$ and thickness $d_1$ and $d_2$ such that $d_2=2 d_1$ and $l>d_2$. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is $\theta_2=2 \theta_1$. If the shear moduli of material 1 is $4 \times 10^9 \mathrm{~N} / \mathrm{m}^2$, then shear moduli of material 2 is $x \times 10^9 \mathrm{~N} / \mathrm{m}^2$, where value of $x$ is ________.

JEE Main 2025 (Online) 4th April Morning Shift
4

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is $n$ times the volume of the bubble $B$, then, the value of $n$ is__________.

JEE Main 2025 (Online) 3rd April Evening Shift
5
The length of a light string is 1.4 m when the tension on it is 5 N . If the tension increases to 7 N , the length of the string is 1.56 m . The original length of the string is__________m.
JEE Main 2025 (Online) 2nd April Evening Shift
6

A steel wire of length 2 m and Young's modulus $2.0 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and $10^{-3}$ respectively, then the elastic potential energy density of the wire is __________ $\times 10^5$ (in SI units).

JEE Main 2025 (Online) 2nd April Morning Shift
7

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of $100 \mathrm{~cm}^2$ with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density $1.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$. What force one needs to apply on the hinged door so that it does not get opened ?

$$\text { (Acceleration due to gravity }=10 \mathrm{~m} / \mathrm{s}^2 \text { ) }$$

JEE Main 2025 (Online) 2nd April Morning Shift
8

The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of $7 \times 10^{6} ~\mathrm{Pa}$, would be __________ $\mathrm{mm}{ }^3$.

(Given bulk modulus of copper $=1.4 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ )

JEE Main 2025 (Online) 28th January Evening Shift
9

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $\left[M^a L^b T^c\right]$. If $b=3$, the value of $c$ is _________.

JEE Main 2025 (Online) 28th January Morning Shift
10

The increase in pressure required to decrease the volume of a water sample by $0.2 \%$ is $\mathrm{P} \times 10^5 \mathrm{Nm}^{-2}$. Bulk modulus of water is $2.15 \times 10^9 \mathrm{Nm}^{-2}$. The value of P is _________ .

JEE Main 2025 (Online) 24th January Evening Shift
11

An air bubble of radius 1.0 mm is observed at a depth 20 cm below the free surface of a liquid having surface tension $0.095 \mathrm{~J} / \mathrm{m}^2$ and density $10^3 \mathrm{~kg} / \mathrm{m}^3$. The difference between pressure inside the bubble and atmospheric pressure is __________ $\mathrm{N} / \mathrm{m}^2$. (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

JEE Main 2025 (Online) 23rd January Evening Shift
12

Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is _________.

JEE Main 2025 (Online) 22nd January Morning Shift
13

Two persons pull a wire towards themselves. Each person exerts a force of $$200 \mathrm{~N}$$ on the wire. Young's modulus of the material of wire is $$1 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$$. Original length of the wire is $$2 \mathrm{~m}$$ and the area of cross section is $$2 \mathrm{~cm}^2$$. The wire will extend in length by _________ $$\mu \mathrm{m}$$.

JEE Main 2024 (Online) 9th April Morning Shift
14

Small water droplets of radius $$0.01 \mathrm{~mm}$$ are formed in the upper atmosphere and falling with a terminal velocity of $$10 \mathrm{~cm} / \mathrm{s}$$. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be ________ $$\mathrm{cm} / \mathrm{s}$$.

JEE Main 2024 (Online) 8th April Evening Shift
15

A liquid column of height $$0.04 \mathrm{~cm}$$ balances excess pressure of a soap bubble of certain radius. If density of liquid is $$8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$$ and surface tension of soap solution is $$0.28 \mathrm{~Nm}^{-1}$$, then diameter of the soap bubble is __________ $$\mathrm{cm}$$. (if $$\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$$ )

JEE Main 2024 (Online) 8th April Morning Shift
16

A wire of cross sectional area A, modulus of elasticity $$2 \times 10^{11} \mathrm{~Nm}^{-2}$$ and length $$2 \mathrm{~m}$$ is stretched between two vertical rigid supports. When a mass of $$2 \mathrm{~kg}$$ is suspended at the middle it sags lower from its original position making angle $$\theta=\frac{1}{100}$$ radian on the points of support. The value of A is ________ $$\times 10^{-4} \mathrm{~m}^2$$ (consider $$x<<\mathrm{L}$$ ).

(given : $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$)

JEE Main 2024 (Online) 6th April Evening Shift Physics - Properties of Matter Question 35 English

JEE Main 2024 (Online) 6th April Evening Shift
17

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $$\frac{10}{x}$$. The value of $$x$$ is ________.

JEE Main 2024 (Online) 6th April Morning Shift
18

JEE Main 2024 (Online) 5th April Evening Shift Physics - Properties of Matter Question 37 English

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of $$10 \mathrm{~N}$$ is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is _________ N.

JEE Main 2024 (Online) 5th April Evening Shift
19

The density and breaking stress of a wire are $$6 \times 10^4 \mathrm{~kg} / \mathrm{m}^3$$ and $$1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2$$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $$\frac{1}{3}^{\text {rd }}$$ of the value on the surface of earth. The maximum length of the wire with breaking is _______ $$\mathrm{m}$$ (take, $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$).

JEE Main 2024 (Online) 5th April Morning Shift
20

Mercury is filled in a tube of radius $$2 \mathrm{~cm}$$ up to a height of $$30 \mathrm{~cm}$$. The force exerted by mercury on the bottom of the tube is _________ N.

(Given, atmospheric pressure $$=10^5 \mathrm{~Nm}^{-2}$$, density of mercury $$=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^{-3}, \mathrm{~g}=10 \mathrm{~m} \mathrm{~s}^{-2}, \pi=\frac{22}{7})$$

JEE Main 2024 (Online) 4th April Evening Shift
21

A soap bubble is blown to a diameter of $$7 \mathrm{~cm}$$. $$36960 \mathrm{~erg}$$ of work is done in blowing it further. If surface tension of soap solution is 40 dyne/$$\mathrm{cm}$$ then the new radius is ________ cm Take $$(\pi=\frac{22}{7})$$.

JEE Main 2024 (Online) 4th April Morning Shift
22

An elastic spring under tension of $$3 \mathrm{~N}$$ has a length $$a$$. Its length is $$b$$ under tension $$2 \mathrm{~N}$$. For its length $$(3 a-2 b)$$, the value of tension will be _______ N.

JEE Main 2024 (Online) 4th April Morning Shift
23
One end of a metal wire is fixed to a ceiling and a load of $2 \mathrm{~kg}$ hangs from the other end. A similar wire is attached to the bottom of the load and another load of $1 \mathrm{~kg}$ hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be ________.

[Area of cross section of wire $=0.005 \mathrm{~cm}^2, \mathrm{Y}=2 \times 10^{11} \mathrm{Nm}^{-2}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2}$ ]
JEE Main 2024 (Online) 1st February Evening Shift
24
A plane is in level flight at constant speed and each of its two wings has an area of $40 \mathrm{~m}^2$. If the speed of the air is $180 \mathrm{~km} / \mathrm{h}$ over the lower wing surface and $252 \mathrm{~km} / \mathrm{h}$ over the upper wing surface, the mass of the plane is ___________ kg.

(Take air density to be $1 \mathrm{~kg} \mathrm{~m}^{-3}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )
JEE Main 2024 (Online) 1st February Morning Shift
25

Two blocks of mass $$2 \mathrm{~kg}$$ and $$4 \mathrm{~kg}$$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $$4.0 \times 10^{-5} \mathrm{~m}$$ and Young's modulus of the metal is $$2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$$. The longitudinal strain developed in the wire is $$\frac{1}{\alpha \pi}$$. The value of $$\alpha$$ is _________. [Use $$g=10 \mathrm{~m} / \mathrm{s}^2$$]

JEE Main 2024 (Online) 31st January Evening Shift Physics - Properties of Matter Question 65 English

JEE Main 2024 (Online) 31st January Evening Shift
26

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $$0.02 \%$$ is _______ $$m$$.

(Take density of sea water $$=10^3 \mathrm{kgm}^{-3}$$, Bulk modulus of rubber $$=9 \times 10^8 \mathrm{~Nm}^{-2}$$, and $$g=10 \mathrm{~ms}^{-2}$$)

JEE Main 2024 (Online) 31st January Morning Shift
27

A big drop is formed by coalescing 1000 small identical drops of water. If $$E_1$$ be the total surface energy of 1000 small drops of water and $$E_2$$ be the surface energy of single big drop of water, then $$E_1: E_2$$ is $$x: 1$$ where $$x=$$ ________.

JEE Main 2024 (Online) 30th January Evening Shift
28

Each of three blocks $$\mathrm{P}, \mathrm{Q}$$ and $$\mathrm{R}$$ shown in figure has a mass of $$3 \mathrm{~kg}$$. Each of the wires $$\mathrm{A}$$ and $$\mathrm{B}$$ has cross-sectional area $$0.005 \mathrm{~cm}^2$$ and Young's modulus $$2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$$. Neglecting friction, the longitudinal strain on wire $$B$$ is ________ $$\times 10^{-4}$$. (Take $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$)

JEE Main 2024 (Online) 30th January Morning Shift Physics - Properties of Matter Question 56 English

JEE Main 2024 (Online) 30th January Morning Shift
29

Two metallic wires $$P$$ and $$Q$$ have same volume and are made up of same material. If their area of cross sections are in the ratio $$4: 1$$ and force $$F_1$$ is applied to $$P$$, an extension of $$\Delta l$$ is produced. The force which is required to produce same extension in $$Q$$ is $$\mathrm{F}_2$$.

The value of $$\frac{F_1}{F_2}$$ is _________.

JEE Main 2024 (Online) 29th January Evening Shift
30

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $$70 \mathrm{~ms}^{-1}$$ and $$65 \mathrm{~ms}^{-1}$$ respectively. If the wing area is $$2 \mathrm{~m}^2$$, the lift of the wing is _________ $$N$$.

(Given density of air $$=1.2 \mathrm{~kg} \mathrm{~m}^{-3}$$)

JEE Main 2024 (Online) 29th January Morning Shift
31

The reading of pressure metre attached with a closed pipe is $$4.5 \times 10^4 \mathrm{~N} / \mathrm{m}^2$$. On opening the valve, water starts flowing and the reading of pressure metre falls to $$2.0 \times 10^4 \mathrm{~N} / \mathrm{m}^2$$. The velocity of water is found to be $$\sqrt{V} \mathrm{~m} / \mathrm{s}$$. The value of $$V$$ is _________.

JEE Main 2024 (Online) 27th January Evening Shift
32

If average depth of an ocean is $$4000 \mathrm{~m}$$ and the bulk modulus of water is $$2 \times 10^9 \mathrm{~Nm}^{-2}$$, then fractional compression $$\frac{\Delta V}{V}$$ of water at the bottom of ocean is $$\alpha \times 10^{-2}$$. The value of $$\alpha$$ is _______ (Given, $$\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$$)

JEE Main 2024 (Online) 27th January Morning Shift
33
There is an air bubble of radius $1.0 \mathrm{~mm}$ in a liquid of surface tension $0.075~ \mathrm{Nm}^{-1}$ and density $1000 \mathrm{~kg} \mathrm{~m}^{-3}$ at a depth of $10 \mathrm{~cm}$ below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _________ $\mathrm{Pa}\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$
JEE Main 2023 (Online) 15th April Morning Shift
34

The elastic potential energy stored in a steel wire of length $$20 \mathrm{~m}$$ stretched through $$2 \mathrm{~cm}$$ is $$80 \mathrm{~J}$$. The cross sectional area of the wire is __________ $$\mathrm{mm}^{2}$$.

$$\left(\right.$$ Given, $$\left.y=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)$$

JEE Main 2023 (Online) 13th April Morning Shift
35

Glycerin of density $$1.25 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$$ is flowing through the conical section of pipe The area of cross-section of the pipe at its ends are $$10 \mathrm{~cm}^{2}$$ and $$5 \mathrm{~cm}^{2}$$ and pressure drop across its length is $$3 ~\mathrm{Nm}^{-2}$$. The rate of flow of glycerin through the pipe is $$x \times 10^{-5} \mathrm{~m}^{3} \mathrm{~s}^{-1}$$. The value of $$x$$ is ___________.

JEE Main 2023 (Online) 12th April Morning Shift
36

The surface tension of soap solution is $$3.5 \times 10^{-2} \mathrm{~Nm}^{-1}$$. The amount of work done required to increase the radius of soap bubble from $$10 \mathrm{~cm}$$ to $$20 \mathrm{~cm}$$ is _________ $$\times ~10^{-4} \mathrm{~J}$$.

$$(\operatorname{take} \pi=22 / 7)$$

JEE Main 2023 (Online) 11th April Evening Shift
37

A wire of density $$8 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$$ is stretched between two clamps $$0.5 \mathrm{~m}$$ apart. The extension developed in the wire is $$3.2 \times 10^{-4} \mathrm{~m}$$. If $$Y=8 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$$, the fundamental frequency of vibration in the wire will be ___________ $$\mathrm{Hz}$$.

JEE Main 2023 (Online) 11th April Evening Shift
38

The length of a wire becomes $$l_{1}$$ and $$l_{2}$$ when $$100 \mathrm{~N}$$ and $$120 \mathrm{~N}$$ tensions are applied respectively. If $$10 ~l_{2}=11~ l_{1}$$, the natural length of wire will be $$\frac{1}{x} ~l_{1}$$. Here the value of $$x$$ is _____________.

JEE Main 2023 (Online) 11th April Morning Shift
39

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $$2.0 \mathrm{~cm}^{2}$$. The area of cross section at the outlet is $$10 \mathrm{~mm}^{2}$$. If the piston is pushed at a speed of $$4 \mathrm{~cm} \mathrm{~s}^{-1}$$, the speed of outgoing fluid is __________ $$\mathrm{cm} \mathrm{s}^{-1}$$

JEE Main 2023 (Online) 10th April Evening Shift Physics - Properties of Matter Question 85 English

JEE Main 2023 (Online) 10th April Evening Shift
40

Two wires each of radius 0.2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is __________ $$\times$$ 10$$^{-6}$$ m. [Young's modulus for steel = 2 $$\times$$ 10$$^{11}$$ Nm$$^{-2}$$ and g = 10 ms$$^{-2}$$ ]

JEE Main 2023 (Online) 10th April Morning Shift Physics - Properties of Matter Question 83 English

JEE Main 2023 (Online) 10th April Morning Shift
41

An air bubble of diameter $$6 \mathrm{~mm}$$ rises steadily through a solution of density $$1750 \mathrm{~kg} / \mathrm{m}^{3}$$ at the rate of $$0.35 \mathrm{~cm} / \mathrm{s}$$. The co-efficient of viscosity of the solution (neglect density of air) is ___________ Pas (given, $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$ ).

JEE Main 2023 (Online) 8th April Morning Shift
42

A metal block of mass $$\mathrm{m}$$ is suspended from a rigid support through a metal wire of diameter $$14 \mathrm{~mm}$$. The tensile stress developed in the wire under equilibrium state is $$7 \times 10^{5} \mathrm{Nm}^{-2}$$. The value of mass $$\mathrm{m}$$ is _________ $$\mathrm{kg}$$. (Take, $$\mathrm{g}=9.8 \mathrm{~ms}^{-2}$$ and $$\pi=\frac{22}{7}$$ )

JEE Main 2023 (Online) 6th April Evening Shift
43

A steel rod has a radius of $$20 \mathrm{~mm}$$ and a length of $$2.0 \mathrm{~m}$$. A force of $$62.8 ~\mathrm{kN}$$ stretches it along its length. Young's modulus of steel is $$2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$$. The longitudinal strain produced in the wire is _____________ $$\times 10^{-5}$$

JEE Main 2023 (Online) 6th April Morning Shift
44

The surface of water in a water tank of cross section area $$750 \mathrm{~cm}^{2}$$ on the top of a house is $$h \mathrm{~m}$$ above the tap level. The speed of water coming out through the tap of cross section area $$500 \mathrm{~mm}^{2}$$ is $$30 \mathrm{~cm} / \mathrm{s}$$. At that instant, $$\frac{d h}{d t}$$ is $$x \times 10^{-3} \mathrm{~m} / \mathrm{s}$$. The value of $$x$$ will be ____________.

JEE Main 2023 (Online) 1st February Evening Shift
45

A certain pressure '$$\mathrm{P}$$' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to $$0.01 \%$$ whereas the liquid gets compressed to $$0.03 \%$$. The ratio of Bulk modulus of water to that of the liquid is $$\frac{3}{x}$$. The value of $$x$$ is ____________.

JEE Main 2023 (Online) 1st February Morning Shift
46

A thin rod having a length of $$1 \mathrm{~m}$$ and area of cross-section $$3 \times 10^{-6} \mathrm{~m}^{2}$$ is suspended vertically from one end. The rod is cooled from $$210^{\circ} \mathrm{C}$$ to $$160^{\circ} \mathrm{C}$$. After cooling, a mass $$\mathrm{M}$$ is attached at the lower end of the rod such that the length of rod again becomes $$1 \mathrm{~m}$$. Young's modulus and coefficient of linear expansion of the rod are $$2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$$ and $$2 \times 10^{-5} \mathrm{~K}^{-1}$$, respectively. The value of $$\mathrm{M}$$ is __________ $$\mathrm{kg}$$.

(Take $$\mathrm{g=10~m~s^{-2}}$$)

JEE Main 2023 (Online) 31st January Morning Shift
47

A metal block of base area 0.20 m$$^2$$ is placed on a table, as shown in figure. A liquid film of thickness 0.25 mm is inserted between the block and the table. The block is pushed by a horizontal force of 0.1 N and moves with a constant speed. IF the viscosity of the liquid is $$5.0\times10^{-3}~\mathrm{Pl}$$, the speed of block is ____________ $$\times10^{-3}$$ m/s.

JEE Main 2023 (Online) 29th January Evening Shift Physics - Properties of Matter Question 111 English

JEE Main 2023 (Online) 29th January Evening Shift
48

A body cools from 60$$^\circ$$C to 40$$^\circ$$C in 6 minutes. If, temperature of surroundings is 10$$^\circ$$C. Then, after the next 6 minutes, its temperature will be ____________$$^\circ$$C.

JEE Main 2023 (Online) 29th January Morning Shift
49

A spherical drop of liquid splits into 1000 identical spherical drops. If u$$_\mathrm{i}$$ is the surface energy of the original drop and u$$_\mathrm{f}$$ is the total surface energy of the resulting drops, the (ignoring evaporation), $${{{u_f}} \over {{u_i}}} = \left( {{{10} \over x}} \right)$$. Then value of x is ____________ :

JEE Main 2023 (Online) 25th January Evening Shift
50

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45$$^\circ$$ with the load axis. The length of wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be $$x\times10^4$$ Nm$$^{-2}$$. The value of $$x$$ is ___________.

JEE Main 2023 (Online) 25th January Morning Shift Physics - Properties of Matter Question 105 English

JEE Main 2023 (Online) 25th January Morning Shift
51

A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is $$3696\times10^{-x}$$ N. The value of $$x$$ is ________.

(Given, g = 9.8 m/s$$^2$$ and $$\pi=\frac{22}{7}$$)

JEE Main 2023 (Online) 24th January Evening Shift
52

A tube of length $$50 \mathrm{~cm}$$ is filled completely with an incompressible liquid of mass $$250 \mathrm{~g}$$ and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $$x \sqrt{F} \,\mathrm{rad} \,\mathrm{s}^{-1}$$. If $$\mathrm{F}$$ be the force exerted by the liquid at the other end then the value of $$x$$ will be __________.

JEE Main 2022 (Online) 29th July Evening Shift
53

A metal wire of length $$0.5 \mathrm{~m}$$ and cross-sectional area $$10^{-4} \mathrm{~m}^{2}$$ has breaking stress $$5 \times 10^{8} \,\mathrm{Nm}^{-2}$$. A block of $$10 \mathrm{~kg}$$ is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _________ $$\mathrm{ms}^{-1}$$.

JEE Main 2022 (Online) 29th July Evening Shift
54

The velocity of a small ball of mass $$0.3 \mathrm{~g}$$ and density $$8 \mathrm{~g} / \mathrm{cc}$$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $$1.3 \mathrm{~g} / \mathrm{cc}$$, then the value of viscous force acting on the ball will be $$x \times 10^{-4} \mathrm{~N}$$, The value of $$x$$ is _________. [use $$\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right]$$

JEE Main 2022 (Online) 29th July Evening Shift
55

The speed of a transverse wave passing through a string of length $$50 \mathrm{~cm}$$ and mass $$10 \mathrm{~g}$$ is $$60 \mathrm{~ms}^{-1}$$. The area of cross-section of the wire is $$2.0 \mathrm{~mm}^{2}$$ and its Young's modulus is $$1.2 \times 10^{11} \mathrm{Nm}^{-2}$$. The extension of the wire over its natural length due to its tension will be $$x \times 10^{-5} \mathrm{~m}$$. The value of $$x$$ is __________.

JEE Main 2022 (Online) 29th July Evening Shift
56

A string of area of cross-section $$4 \mathrm{~mm}^{2}$$ and length $$0.5 \mathrm{~m}$$ is connected with a rigid body of mass $$2 \mathrm{~kg}$$. The body is rotated in a vertical circular path of radius $$0.5 \mathrm{~m}$$. The body acquires a speed of $$5 \mathrm{~m} / \mathrm{s}$$ at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _________ $$ \times 10^{-5}$$.

(use Young's modulus $$10^{11} \mathrm{~N} / \mathrm{m}^{2}$$ and $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$$)

JEE Main 2022 (Online) 28th July Evening Shift
57

The diameter of an air bubble which was initially $$2 \mathrm{~mm}$$, rises steadily through a solution of density $$1750 \mathrm{~kg} \mathrm{~m}^{-3}$$ at the rate of $$0.35 \,\mathrm{cms}^{-1}$$. The coefficient of viscosity of the solution is _________ poise (in nearest integer). (the density of air is negligible).

JEE Main 2022 (Online) 28th July Morning Shift
58

In an experiment to determine the Young's modulus, steel wires of five different lengths $$(1,2,3,4$$, and $$5 \mathrm{~m})$$ but of same cross section $$\left(2 \mathrm{~mm}^{2}\right)$$ were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $$x \times 10^{11} \,\mathrm{Nm}^{-2}$$, then the value of $$x$$ is __________.

JEE Main 2022 (Online) 27th July Evening Shift Physics - Properties of Matter Question 135 English

JEE Main 2022 (Online) 27th July Evening Shift
59

A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is ___________.

JEE Main 2022 (Online) 27th July Evening Shift
60

A square aluminum (shear modulus is $$25 \times 10^{9}\, \mathrm{Nm}^{-2}$$) slab of side $$60 \mathrm{~cm}$$ and thickness $$15 \mathrm{~cm}$$ is subjected to a shearing force (on its narrow face) of $$18.0 \times 10^{4}$$ $$\mathrm{N}$$. The lower edge is riveted to the floor. The displacement of the upper edge is ____________ $$\mu$$m.

JEE Main 2022 (Online) 27th July Morning Shift
61

A uniform heavy rod of mass $$20 \mathrm{~kg}$$, cross sectional area $$0.4 \mathrm{~m}^{2}$$ and length $$20 \mathrm{~m}$$ is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is $$x \times 10^{-9} \mathrm{~m}$$. The value of $$x$$ is _______________.

(Given, young modulus Y = 2 $$\times$$ 1011 Nm$$-$$2 and g = 10 ms$$-$$2)

JEE Main 2022 (Online) 26th July Evening Shift
62

In an experiment to determine the Young's modulus of wire of a length exactly $$1 \mathrm{~m}$$, the extension in the length of the wire is measured as $$0.4 \mathrm{~mm}$$ with an uncertainty of $$\pm\, 0.02 \mathrm{~mm}$$ when a load of $$1 \mathrm{~kg}$$ is applied. The diameter of the wire is measured as $$0.4 \mathrm{~mm}$$ with an uncertainty of $$\pm \,0.01 \mathrm{~mm}$$. The error in the measurement of Young's modulus $$(\Delta \mathrm{Y})$$ is found to be $$x \times 10^{10}\, \mathrm{Nm}^{-2}$$. The value of $$x$$ is _________________. $$\left(\right.$$take $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$ )

JEE Main 2022 (Online) 26th July Morning Shift
63

A wire of length $$\mathrm{L}$$ and radius $$\mathrm{r}$$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $$\mathrm{F}$$, its length increases by $$5 \mathrm{~cm}$$. Another wire of the same material of length $$4 \mathrm{L}$$ and radius $$4 \mathrm{r}$$ is pulled by a force $$4 \mathrm{F}$$ under same conditions. The increase in length of this wire is __________________ $$\mathrm{cm}$$.

JEE Main 2022 (Online) 25th July Morning Shift
64

The excess pressure inside a liquid drop is 500 Nm$$-$$2. If the radius of the drop is 2 mm, the surface tension of liquid is x $$\times$$ 10$$-$$3 Nm$$-$$1. The value of x is _____________.

JEE Main 2022 (Online) 30th June Morning Shift
65

A small spherical ball of radius 0.1 mm and density 104 kg m$$-$$3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be ___________ m.

(Given g = 10 ms$$-$$2, viscosity of water = 1.0 $$\times$$ 10$$-$$5 N-sm$$-$$2).

JEE Main 2022 (Online) 29th June Evening Shift
66

A liquid of density 750 kgm$$-$$3 flows smoothly through a horizontal pipe that tapers in cross-sectional area from A1 = 1.2 $$\times$$ 10$$-$$2 m2 to A2 = $${{{A_1}} \over 2}$$. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ___________ $$\times$$ 10$$-$$3 m3s$$-$$1.

JEE Main 2022 (Online) 28th June Evening Shift
67

The area of cross-section of a large tank is 0.5 m2. It has a narrow opening near the bottom having area of cross-section 1 cm2. A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is 40 cm above the bottom, will be ___________ cms$$-$$1. [Take g = 10 ms$$-$$2]

JEE Main 2022 (Online) 27th June Morning Shift
68

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 $$\times$$ 10$$-$$4 is __________ kJ/m3. Assume that material is elastic upto the linear strain of 5 $$\times$$ 10$$-$$4.

JEE Main 2022 (Online) 26th June Morning Shift Physics - Properties of Matter Question 156 English

JEE Main 2022 (Online) 26th June Morning Shift
69

The elongation of a wire on the surface of the earth is 10$$-$$4 m. The same wire of same dimensions is elongated by 6 $$\times$$ 10$$-$$5 m on another planet. The acceleration due to gravity on the planet will be ____________ ms$$-$$2. (Take acceleration due to gravity on the surface of earth = 10 ms$$-$$2)

JEE Main 2022 (Online) 26th June Morning Shift
70

An ideal fluid of density 800 kgm$$-$$3, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to $${a \over 2}$$. The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is $${{\sqrt x } \over 6}$$ ms$$-$$1 for x = ___________. (Given g = 10 ms$$-$$2)

JEE Main 2022 (Online) 26th June Morning Shift Physics - Properties of Matter Question 154 English

JEE Main 2022 (Online) 26th June Morning Shift
71

The velocity of upper layer of water in a river is 36 kmh$$-$$1. Shearing stress between horizontal layers of water is 10$$-$$3 Nm$$-$$2. Depth of the river is __________ m. (Co-efficient of viscosity of water is 10$$-$$2 Pa.s)

JEE Main 2022 (Online) 25th June Morning Shift
72

In an experiment to verify Newton's law of cooling, a graph is plotted between the temperature difference ($$\Delta$$T) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as 80$$^\circ$$C. The value of t2 as mentioned in the graph will be __________.

JEE Main 2022 (Online) 24th June Evening Shift Physics - Properties of Matter Question 150 English

JEE Main 2022 (Online) 24th June Evening Shift
73
A steel rod with y = 2.0 $$\times$$ 1011 Nm$$-$$2 and $$\alpha$$ = 10$$-$$5 $$^\circ$$C$$-$$1 of length 4 m and area of cross-section 10 cm2 is heated from 0$$^\circ$$C to 400$$^\circ$$C without being allowed to extend. The tension produced in the rod is x $$\times$$ 105 N where the value of x is ____________.
JEE Main 2021 (Online) 1st September Evening Shift
74
When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases by 0.5%.

(The bulk modulus of rubber = 9.8 $$\times$$ 108 Nm$$-$$2, Density of sea water = 103 kgm$$-$$3, g = 9.8 m/s2)
JEE Main 2021 (Online) 31st August Morning Shift
75
Wires W1 and W2 are made of same material having the breaking stress of 1.25 $$\times$$ 109 N/m2. W1 and W2 have cross-sectional area of 8 $$\times$$ 10$$-$$7 m2 and 4 $$\times$$ 10$$-$$7 m2, respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is ____________ kg. (Use g = 10 m/s2)

JEE Main 2021 (Online) 27th August Evening Shift Physics - Properties of Matter Question 171 English
JEE Main 2021 (Online) 27th August Evening Shift
76
A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ................ cm.
JEE Main 2021 (Online) 26th August Morning Shift
77
The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth 'h' below the water level. The value of 'h' for which the emerging steam of water strikes the ground at the maximum range is ________ m.
JEE Main 2021 (Online) 27th July Evening Shift
78
A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10$$-$$6 m2 stretched by an amount 0.04 m. The velocity of the projected stone is ______________ m/s.

(Young's modulus of rubber = 0.5 $$\times$$ 109 N/m2)
JEE Main 2021 (Online) 27th July Morning Shift
79
In 5 minutes, a body cools from 75$$^\circ$$C to 65$$^\circ$$C at room temperature of 25$$^\circ$$C. The temperature of body at the end of next 5 minutes is _________$$^\circ$$ C.
JEE Main 2021 (Online) 22th July Evening Shift
80
Consider a water tank as shown in the figure. It's cross-sectional area is 0.4 m2. The tank has an opening B near the bottom whose cross-section area is 1 cm2. A load of 24 kg is applied on the water at the top when the height of the water level is 40 cm above the bottom, the velocity of water coming out the opening B is v ms-1.

The value of v, to the nearest integer, is ___________. [Take value of g to be 10 ms-2]

JEE Main 2021 (Online) 18th March Evening Shift Physics - Properties of Matter Question 187 English
JEE Main 2021 (Online) 18th March Evening Shift
81
Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires A and B are in the ratio of a : b. Then a/b can be expressed as 1/x where x is _________.
JEE Main 2021 (Online) 18th March Morning Shift
82
Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01 cm3 of oleic acid per cm3 of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4 cm2 by considering 100 spherical drops of radius $${\left( {{3 \over {40\pi }}} \right)^{{1 \over 3}}} \times {10^{ - 3}}$$ cm. Then the thickness of oleic acid layer will be x $$\times$$ 10$$-$$14 m. Where x is ____________.
JEE Main 2021 (Online) 17th March Evening Shift
83
A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm.
JEE Main 2021 (Online) 24th February Evening Shift
84
A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It can lift ___________ kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass 'm' on the smaller piston.
JEE Main 2021 (Online) 24th February Morning Shift
85
When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to 0o, the surface tension of the liquid, in milliNewton m–1, is [$$\rho $$(liquid) = 900 kgm–3, g = 10 ms–2]
(Give answer in closest integer) _____.
JEE Main 2020 (Online) 3rd September Morning Slot
86
A wire of density 9 $$ \times $$ 10–3 kg cm–3 is stretched between two clamps 1 m apart. The resulting strain in the wire is 4.9 $$ \times $$ 10–4. The lowest frequency of the transverse vibrations in the wire is : (Young’s modulus of wire Y = 9 $$ \times $$ 1010 Nm–2), (to the nearest integer), _________
JEE Main 2020 (Online) 2nd September Evening Slot
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