## Numerical

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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 ...
JEE Main 2021 (Online) 1st September Evening Shift
When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases by 0.5%. (The bulk modulus of ru...
JEE Main 2021 (Online) 31st August Morning Shift
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-s...
JEE Main 2021 (Online) 27th August Evening Shift
A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap b...
JEE Main 2021 (Online) 26th August Morning Shift
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 dep...
JEE Main 2021 (Online) 27th July Evening Shift
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...
JEE Main 2021 (Online) 27th July Morning Shift
The area of cross-section of a railway track is 0.01 m2. The temperature variation is 10$$^\circ$$C. Coefficient of line...
JEE Main 2021 (Online) 22th July Evening Shift
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 bo...
JEE Main 2021 (Online) 18th March Evening Shift
Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01 cm3 of oleic ac...
JEE Main 2021 (Online) 17th March Evening Shift
A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It can lift ___________ kg when the d...
JEE Main 2021 (Online) 24th February Morning Slot
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 ...
JEE Main 2020 (Online) 3rd September Morning Slot
A wire of density 9 $$\times$$ 10–3 kg cm–3 is stretched between two clamps 1 m apart. The resulting strain in the wir...
JEE Main 2020 (Online) 2nd September Evening Slot
A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the sp...
JEE Main 2020 (Online) 8th January Morning Slot

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A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bo...
JEE Main 2021 (Online) 31st August Evening Shift
Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $$\times$$ 103 kg. The inner ...
JEE Main 2021 (Online) 31st August Evening Shift
A uniform heavy rod of weight 10 kg ms$$-$$2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed supp...
JEE Main 2021 (Online) 31st August Morning Shift
In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 $$\times$$ 10$$-$$5 m...
JEE Main 2021 (Online) 27th August Morning Shift
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 ...
JEE Main 2021 (Online) 26th August Evening Shift
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-...
JEE Main 2021 (Online) 26th August Morning Shift
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 sp...
JEE Main 2021 (Online) 27th July Evening Shift
A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is mad...
JEE Main 2021 (Online) 27th July Morning Shift
Two series of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two w...
JEE Main 2021 (Online) 25th July Morning Shift
Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy befo...
JEE Main 2021 (Online) 20th July Evening Shift
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 diff...
JEE Main 2021 (Online) 20th July Morning Shift
An object is located at 2 km beneath the surface of the water. If the fractional compression $${{\Delta V} \over V}$$ is...
JEE Main 2021 (Online) 17th March Evening Shift
When two soap bubbles of radii a and b (b &gt; a) coalesce, the radius of curvature of common surface is :
JEE Main 2021 (Online) 17th March Morning Shift
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...
JEE Main 2021 (Online) 16th March Evening Shift
The pressure acting on a submarine is 3 $$\times$$ 105 Pa at a certain depth. If the depth is doubled, the percentage in...
JEE Main 2021 (Online) 16th March Morning Shift
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 ...
JEE Main 2021 (Online) 26th February Evening Shift
The normal density of a material is $$\rho$$ and its bulk modulus of elasticity is K. The magnitude of increase in densi...
JEE Main 2021 (Online) 26th February Morning Shift
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 mec...
JEE Main 2021 (Online) 26th February Morning Shift
If Y, K and $$\eta$$ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respective...
JEE Main 2021 (Online) 24th February Morning Slot
A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms–1 at a point where the pressure i...
JEE Main 2020 (Online) 6th September Evening Slot
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 ...
JEE Main 2020 (Online) 6th September Morning Slot
In an experiment to verify Stokes law, a small spherical ball of radius r and density $$\rho$$ falls under gravity thro...
JEE Main 2020 (Online) 5th September Evening Slot
Assume that the displacement(s) of air is proportional to the pressure difference ($$\Delta$$p) created by a sound wave...
JEE Main 2020 (Online) 5th September Morning Slot
A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell ...
JEE Main 2020 (Online) 5th September Morning Slot
Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the ...
JEE Main 2020 (Online) 4th September Evening Slot
A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the length of the side of the ...
JEE Main 2020 (Online) 4th September Evening Slot
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 ...
JEE Main 2020 (Online) 4th September Morning Slot
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
A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface ...
JEE Main 2020 (Online) 2nd September Evening Slot
A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the...
JEE Main 2020 (Online) 2nd September Morning Slot
Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored...
JEE Main 2020 (Online) 9th January Evening Slot
A small spherical droplet of density d is floating exactly half immersed in a liquid of density $$\rho$$ and surface te...
JEE Main 2020 (Online) 9th January Evening Slot
Water flows in a horizontal tube (see figure). The pressure of water changes by 700 Nm–2 between A and B where the area ...
JEE Main 2020 (Online) 9th January Morning Slot
Two liquids of densities $${\rho _1}$$ an $${\rho _2}$$ ($${\rho _2}$$ = 2$${\rho _1}$$) are filled up behind a square w...
JEE Main 2020 (Online) 8th January Evening Slot
A leak proof cylinder of length 1m, made of a metal which has very low coefficient of expansion is floating vertically i...
JEE Main 2020 (Online) 8th January Morning Slot
Consider a solid sphere of radius R and mass density $$\rho \left( r \right) = {\rho _0}\left( {1 - {{{r^2}} \over {{R^2... JEE Main 2020 (Online) 8th January Morning Slot An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pip... JEE Main 2020 (Online) 7th January Evening Slot A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity equals Y... JEE Main 2019 (Online) 12th April Evening Slot The number density of molecules of a gas depends on their distance r from the origin as,$$n\left( r \right) = {n_0}{e^{...
JEE Main 2019 (Online) 12th April Evening Slot
A solid sphere, of radius R acquires a terminal velocity v1 when falling (due to gravity) through a viscous fluid having...
JEE Main 2019 (Online) 12th April Evening Slot
At 40o C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. W...
JEE Main 2019 (Online) 12th April Morning Slot
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 lo...
JEE Main 2019 (Online) 10th April Evening Slot
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...
JEE Main 2019 (Online) 10th April Evening Slot
In an experiment, brass and steel wires of length 1 m each with areas of cross section 1mm2 are used. The wires are con...
JEE Main 2019 (Online) 10th April Evening Slot
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, i...
JEE Main 2019 (Online) 10th April Evening Slot
Water from a tap emerges vertically downwards with an initial speed of 1.0 ms–1 . The cross-sectional area of the tap is...
JEE Main 2019 (Online) 10th April Evening Slot
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 ...
JEE Main 2019 (Online) 10th April Morning Slot
Two materials having coefficients of thermal conductivity '3K' and 'K' and thickness 'd' and '3d', respectively, are joi...
JEE Main 2019 (Online) 9th April Evening Slot
A wooden block floating in a bucket of water has 4/5 of its volume submerged. When certain amount of an oil is poured in...
JEE Main 2019 (Online) 9th April Evening Slot
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 capill...
JEE Main 2019 (Online) 9th April Morning Slot
A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liqui...
JEE Main 2019 (Online) 9th April Morning Slot
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 an...
JEE Main 2019 (Online) 8th April Evening Slot
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, w...
JEE Main 2019 (Online) 8th April Morning Slot
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 f...
JEE Main 2019 (Online) 8th April Morning Slot
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....
JEE Main 2019 (Online) 8th April Morning Slot
A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. Th...
JEE Main 2019 (Online) 12th January Evening Slot
A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. T...
JEE Main 2019 (Online) 12th January Evening Slot
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 ...
JEE Main 2019 (Online) 12th January Evening Slot
A liquid of density $$\rho$$ is coming out of a hose pipe of radius a with horizontal speed $$\upsilon$$ and hits a me...
JEE Main 2019 (Online) 11th January Morning Slot
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 cm...
JEE Main 2019 (Online) 10th January Morning Slot
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...
JEE Main 2019 (Online) 9th January Evening Slot
A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of lin...
JEE Main 2019 (Online) 9th January Morning Slot
A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P2 be the pr...
JEE Main 2018 (Online) 16th April Morning Slot
A body takes 10 minutes to cool from 60oC to 50oC. The tempertature of surroundings is constant at 25oC. Then, the tempe...
JEE Main 2018 (Online) 15th April Evening Slot
As shown in the figure, forces of 105 N each are applied in opposite directions, on the upper and lower faces of a cube...
JEE Main 2018 (Online) 15th April Evening Slot
The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms-1 is : [kB =1.4 $$\times... JEE Main 2018 (Online) 15th April Evening Slot When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes$${{5r} \over 4}.$$Tak... JEE Main 2018 (Online) 15th April Evening Slot A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical containe... JEE Main 2018 (Offline) Two tubes of radii r1 and r2, and lengths l1 and l2 , respectively, are connected in series and a liquid flows through ... JEE Main 2017 (Online) 9th April Morning Slot A steel rail of length 5 m and area of cross section 40cm2 is prevented from expanding along its length while the tempe... JEE Main 2017 (Online) 9th April Morning Slot A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its ... JEE Main 2017 (Online) 8th April Morning Slot In an experiment, a sphere of aluminium of mass 0.20 kg is heated upto 150oC. Immediately, it is put into water of volum... JEE Main 2017 (Online) 8th April Morning Slot An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the bulk modulu... JEE Main 2017 (Offline) A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 17... JEE Main 2017 (Offline) A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains sa... JEE Main 2017 (Offline) A bottle has an opening of radius a and length b. A cork of length b and radius (a +$$\Delta $$a) where ($$\Delta $$a &... JEE Main 2016 (Online) 10th April Morning Slot A thin 1 m long rod has a radius of 5 mm. A force of 50$$\pi $$kN is applied at one end to determine its Young’s modulu... JEE Main 2016 (Online) 10th April Morning Slot Which of the following option correctly describes the variation of the speed v and acceleration ‘a’ of a point mass fall... JEE Main 2016 (Online) 9th April Morning Slot Consider a water jar of radius R that has water filled up to height H and is kept on astand of height h (see figure). T... JEE Main 2016 (Online) 9th April Morning Slot A uniformly tapering conical wire is made from a material of Young’s modulus Y and has a normal, unextended length L. Th... JEE Main 2016 (Online) 9th April Morning Slot A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at T=0oC. If the te... JEE Main 2016 (Online) 9th April Morning Slot On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of ra... JEE Main 2014 (Offline) An open glass tube is immersed in mercury in such a way that a length of$$8cm$$extends above the mercury level. T... JEE Main 2014 (Offline) Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. W... JEE Main 2013 (Offline) A uniform cylinder of length$$L$$and mass$$M$$having cross-sectional area$$A$$is suspended, with its length vertic... JEE Main 2013 (Offline) A thin liquid film formed between a U-shaped wire and a light slider supports a weight of$$1.5 \times {10^{ - 2}}\,\,N\$...
AIEEE 2012
Water is flowing continuously from a tap having an internal diameter $$8 \times {10^{ - 3}}\,\,m.$$ The water velocity a...
AIEEE 2011
Work done in increasing the size of a soap bubble from a radius of $$3$$ $$cm$$ to $$5$$ $$cm$$ is nearly (Surface tensi...
AIEEE 2011
A ball is made of a material of density $$\rho$$ where $${\rho _{oil}}\, &lt; \rho &lt; {\rho _{water}}$$ with $${\rho... AIEEE 2010 Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of$${30^ \circ }$$w... AIEEE 2010 Two wires are made of the same material and have the same volume. However wire$$1$$has cross-sectional area$$A$$and ... AIEEE 2009 A jar is filled with two non-mixing liquids$$1$$and$$2$$having densities$${\rho _1}$$and$${\rho _2}$$respective... AIEEE 2008 A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the fol... AIEEE 2008 A spherical solid ball of volume$$V$$is made of a material of density$${\rho _1}$$. It is falling through a liquid of... AIEEE 2008 A wire elongates by$$lmm$$when a LOAD$$W$$is hanged from it. If the wire goes over a pulley and two weights$$W...
AIEEE 2006
If the terminal speed of a sphere of gold (density $$= 19.5\,\,kg/{m^3}$$) is $$0.2$$ $$m/s$$ in a viscous liquid (dens...
AIEEE 2006
A $$20$$ $$cm$$ long capillary tube is dipped in water. The water rises up to $$8$$ $$cm.$$ If the entire arrangement is...
AIEEE 2005
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
A radiation of energy $$E$$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is...
AIEEE 2004
If two soap bubbles of different radii are connected by a tube
AIEEE 2004
Spherical balls of radius $$R$$ are falling in a viscous fluid of viscosity $$\eta$$ with a velocity $$v.$$ The retardi...
AIEEE 2004
A wire fixed at the upper end stretches by length $$l$$ by applying a force $$F.$$ The work done in stretching is
AIEEE 2004
A cylinder of height $$20$$ $$m$$ is completely filled with water. The velocity of efflux of water (in $$m{s^{ - 1}}$$) ...
AIEEE 2002

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