## MCQ (Single Correct Answer)

A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :

With rise in temperature, the Young's modulus of elasticity :

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

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...

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-sectio...

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...

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 radi...

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 ...

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 vi...

Given below are two statements :
Statement (I) :Viscosity of gases is greater than that of liquids.
Statement (II) : Surface tension of a liquid decre...

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 increas...

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

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at $$\mathrm{A}$$ is...

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 v...

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

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...

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 sa...

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 pr...

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...

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}...

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 un...

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 s...

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 ...

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} / \m...

The average kinetic energy of a molecule of the gas is

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 g...

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...

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 am...

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 d...

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...

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 dip...

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

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/...

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 $$3.5 \mathrm{~cm}$$...

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 ty...

Match List I with List II
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.tg td{border-color:black;border-style:solid;border-width:1px;font-family...

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 t...

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 o...

The frequency ($$\nu$$) of an oscillating liquid drop may depend upon radius ($$r$$) of the drop, density ($$\rho$$) of liquid and the surface tension...

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...

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 gr...

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 :...

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} / \mathr...

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...

A balloon has mass of $$10 \mathrm{~g}$$ in air. The air escapes from the balloon at a uniform rate with velocity $$4.5 \mathrm{~cm} / \mathrm{s}$$. I...

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 \ti...

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...

Two cylindrical vessels of equal cross-sectional area $$16 \mathrm{~cm}^{2}$$ contain water upto heights $$100 \mathrm{~cm}$$ and $$150 \mathrm{~cm}$$...

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 cr...

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...

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$$-$$...

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...

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...

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...

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 $$\tim...

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 ...

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 ...

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 th...

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 de...

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 Re...

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

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 pos...

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

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...

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 mate...

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 $$\times$$ 10...

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 } \...

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 t...

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 an...

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...

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 bod...

Two spherical soap bubbles of radii r1 and r2 in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to :...

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 combina...

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 :...

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 :

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...

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...

When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface is :

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 vi...

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 ...

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 :...

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 ...

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 pressur...

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 relatio...

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 w...

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....

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...

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 ...

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...

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 ...

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 o...

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 w...

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their
volumes is :

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 =...

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 ...

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 dro...

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...

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 an...

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 f...

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 \l...

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 h...

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, resp...

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 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 ...

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 t...

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 pres...

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....

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 o...

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 full...

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 elast...

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, ar...

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 tha...

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 i...

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 :

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 ...

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 weighin...

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...

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...

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...

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 ...

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...

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 t...

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...

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 ra...

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...

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...

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 t...

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 u...

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 ...

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 ...

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 co...

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...

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 ex...

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 f...

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 lowe...

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 &l...

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 me...

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 the...

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 ...

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 circul...

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 liqui...

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 ma...

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...

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 ...

A liquid in a beaker has temperature $$\theta \left( t \right)$$ at time $$t$$ and $${\theta _0}$$ is temperature of surroundings, then according to N...

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...

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\,...

A ball is made of a material of density $$\rho $$ where $${\rho _{oil}}\, < \rho < {\rho _{water}}$$ with $${\rho _{oil}}$$ and $${\rho _{water...

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...

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( {{\...

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 natu...

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 ma...

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 $$ = 1.5\,\,kg/{m^3}$$, fi...

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 en...

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

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 eleva...

A wire fixed at the upper end stretches by length $$l$$ by applying a force $$F.$$ The work done in stretching is

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...

If two soap bubbles of different radii are connected by a tube

According to Newton's law of cooling, the rate of cooling of a body is proportional to $${\left( {\Delta \theta } \right)^n},$$ where $${\Delta \thet...

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 si...

## Numerical

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...

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}...

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 o...

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 ...

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$...

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 $$\mathrm{A}$$ ...

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 fo...

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $$70 \mathrm{~ms}^{-1}$$ an...

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 flowin...

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...

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...

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...

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 t...

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 bubb...

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...

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...

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 ...

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 o...

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...

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 develo...

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. Y...

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. Th...

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 th...

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. T...

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...

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 t...

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{...

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 pas...

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...

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 ...

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}^{-...

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...

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 are...

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...

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...

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 sectio...

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 o...

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 sub...

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 su...

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 a...

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...

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...

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. I...

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...

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 ap...

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 $$\times$$ ...

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 anothe...

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 \o...

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...

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 ...

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...

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$$...

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 $$\times$$ ...

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 exces...

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. ...

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 velo...

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 minu...

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 ...

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...

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. Th...

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...

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 i...

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
betwe...

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. Th...