Mechanical Properties of Fluids
69 JEE Physics previous year questions on Mechanical Properties of Fluids — options free on every question; 7 include the answer & explanation free, the rest unlock with PYQ Pass.
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, 28 Jan (Shift 1)]
C, D, E only
Surface tension is property of surface molecules not interior molecules. In case of liquid as temperature increases surface tension decreases. In case of gases due to increase in temperature collision will be more frequent hence viscosity increases.
A liquid of density \(600kg/{m}^{3}\) flowing steadily in a tube of varying cross-section. The cross-section at a point A is \(1.0c{m}^{2}\) and that at B is \(20m{m}^{2}\). Both the points A and B are in same horizontal plane, the speed of the liquid at A is 10 cm / s. The difference in pressures at A and B points is _______ Pa.
[JEE Main 2026, 8 Apr (Shift 2)]
72
Given:
\({A}_{1}=1.0c{m}^{2},{A}_{2}=20m{m}^{2}=0.2c{m}^{2}\)
Using continuity equation:
\({A}_{1}{v}_{1}={A}_{2}{v}_{2}\)
\(1\times 10=0.2\times {v}_{2}\Rightarrow {v}_{2}=50cm/s\)
Using Bernoulli’s theorem at the same horizontal level:
\({P}_{1}+\frac{1}{2}\rho {v}_{1}^{2}={P}_{2}+\frac{1}{2}\rho {v}_{2}^{2}\)
\({P}_{1}-{P}_{2}=\frac{1}{2}\rho \left({v}_{2}^{2}-{v}_{1}^{2}\right)\)
Convert to SI:
\({v}_{1}=0.1m/s,{v}_{2}=0.5m/s\)
\({P}_{1}-{P}_{2}=\frac{1}{2}(600)\left(0.{5}^{2}-0.{1}^{2}\right)=72Pa\)
An air bubble at a depth of 20 cm in water has a radius of 1 mm. If the inner pressure of the bubble is greater than the atmospheric pressure by \(2100\mathrm{N}/{\mathrm{m}}^{2}\), find the surface tension of the bubble.
\(\text{0.05 }\text{N/m}\)
Here, Pi - Po = 2100 ... (1)
Let the pressure at the depth is Po'.
\({\mathrm{P}}_{\mathrm{o}}^{'}={\mathrm{P}}_{\mathrm{o}}+\rho \mathrm{g}\mathrm{h}\\ \mathrm{So},\\ {\mathrm{P}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{o}}^{'}=\frac{2\mathrm{T}}{\mathrm{R}}\\ {\mathrm{P}}_{\mathrm{i}}={\mathrm{P}}_{\mathrm{o}}+\rho \mathrm{g}\mathrm{h}+\frac{2\mathrm{T}}{\mathrm{R}}\\ {\mathrm{P}}_{\mathrm{o}}+2100={\mathrm{P}}_{\mathrm{o}}+1000\times 10\times 0.2+\frac{2\mathrm{T}}{{10}^{-3}}\)
\(100=\frac{2T}{R}\)
\(\Rightarrow T=\frac{100\times {10}^{-2}}{20}\)
= 0.05 N/m
If an air bubble of diameter 2 mm rises steadily through a liquid of density \(2000kg/{m}^{3}\) at a rate of \(0.5cm/s\), then the coefficient of viscosity of liquid is ________ Poise. (Take \(g=10m/{s}^{2}\) )
[02 April, 2026 (Shift-2)]
8.8
For steady rise, viscous force balances buoyant force:
\(6\pi \eta rv=\frac{4}{3}\pi {r}^{3}\rho g\)
\(\eta =\frac{2{r}^{2}\rho g}{9v}\)
\(r=1mm={10}^{-3}m,v=0.5cm/s=5\times {10}^{–3}m/s\)
\(\eta =\frac{2{\left({10}^{-3}\right)}^{2}\times 2000\times 10}{9\cdot 5\times {10}^{-3}}=\frac{2\times {10}^{-6}\times 20000}{45\times {10}^{-3}}\)
\(=\frac{0.04}{0.045}\approx 0.88Pa=8.8\) poise
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, 23 Jan (Shift 2)]
\(\sqrt{{P}_{1}-{P}_{2}}\)
\(\text{ Apply Bernoulli's eqn }\\ \frac{{P}_{1}}{\rho g}+\frac{{V}_{1}^{2}}{2g}=\frac{{P}_{2}}{\rho g}+\frac{{V}_{2}^{2}}{2g}\\ \frac{{P}_{1}}{\rho g}+0=\frac{{P}_{2}}{\rho g}+\frac{{V}^{2}}{2g}\\ V=\sqrt{\frac{2\left({P}_{1}-{P}_{2}\right)}{\rho }}\\ V\propto \sqrt{\left({P}_{1}-{P}_{2}\right)}\)
An air bubble at a depth of 20 cm in water has a radius of 1 mm. If the inner pressure of the bubble is greater than the atmospheric pressure by \(2100\mathrm{N}/{\mathrm{m}}^{2}\), find the surface tension of the bubble.
\(\text{0.05 }\text{N/m}\)
Here, Pi - Po = 2100 ... (1)
Let the pressure at the depth is Po'.
\({\mathrm{P}}_{\mathrm{o}}^{'}={\mathrm{P}}_{\mathrm{o}}+\rho \mathrm{g}\mathrm{h}\\ \mathrm{So},\\ {\mathrm{P}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{o}}^{'}=\frac{2\mathrm{T}}{\mathrm{R}}\\ {\mathrm{P}}_{\mathrm{i}}={\mathrm{P}}_{\mathrm{o}}+\rho \mathrm{g}\mathrm{h}+\frac{2\mathrm{T}}{\mathrm{R}}\\ {\mathrm{P}}_{\mathrm{o}}+2100={\mathrm{P}}_{\mathrm{o}}+1000\times 10\times 0.2+\frac{2\mathrm{T}}{{10}^{-3}}\)
\(100=\frac{2T}{R}\)
\(\Rightarrow T=\frac{100\times {10}^{-2}}{20}\)
= 0.05 N/m
A sphere of mass \(M\) is dropped into glycerin. The density of glycerin is half the density of the sphere. After some time, the sphere moves down with constant velocity. What is the viscous force acting on the sphere?
(Shift II Memory Based)
\(\frac{Mg}{2}\)
At terminal velocity (constant velocity), the net force acting on the sphere is zero. The forces acting on the sphere are:
- Gravitational Force (\({F}_{g}\)): Downward force due to the weight of the sphere. \({F}_{g}=Mg\)
- Buoyant Force (\({F}_{b}\)): Upward force due to the displaced glycerin. \({F}_{b}={\rho }_{\text{glycerin}}Vg\) where \({\rho }_{\text{glycerin}}\)is the density of glycerin, \(V\) is the volume of the sphere, and \(g\) is the acceleration due to gravity.
- Viscous Force (\({F}_{v}\)): Upward force due to the viscosity of glycerin. This balances the remaining downward force at terminal velocity.
From equilibrium at terminal velocity:
\({F}_{v}={F}_{g}−{F}_{b}\)
Step 1: Relationship Between DensitiesThe density of glycerin (\({\rho }_{\text{glycerin}}\)) is half the density of the sphere (\({\rho }_{\text{sphere}}\)):
\({\rho }_{\text{glycerin}}=\frac{{\rho }_{\text{sphere}}}{2}\)
The mass \(M\) of the sphere is related to its density and volume:
\(M={\rho }_{\text{sphere}}V\)
Substitute \({\rho }_{\text{glycerin}}=\frac{{\rho }_{\text{sphere}}}{2}\) into \({F}_{b}\):
\({F}_{b}=\frac{{\rho }_{\text{sphere}}}{2}Vg=\frac{M}{2}g\)
Step 2: Calculate the Viscous ForceUsing \({F}_{v}={F}_{g}−{F}_{b}\):
\({F}_{v}=Mg−\frac{M}{2}g\)
Simplify:
\({F}_{v}=\frac{M}{2}g\)
Final Answer:The viscous force acting on the sphere is:
\(\frac{Mg}{2}\)
A horizontal pipe of variable cross-section has a fluid of density \(\rho\) flowing through it. At cross-sections A and B, the velocities are \({V}_{A}\) and \({V}_{B}\), and the pressures are \({P}_{A}\) and \({P}_{B}\). Find the correct relation between velocities.
(Shift - II Memory Based)
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An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density \(1000kg/{m}^{3}\). If the pressure inside the bubble is \(2100N/{m}^{2}\) greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use g\(=10m/{s}^{2}\))
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A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is \(y\pi \times {10}^{-2}\mathrm{s}\), where the value of \(y\) is
(Acceleration due to gravity, \(g=10\mathrm{m}/{\mathrm{s}}^{2}\), density of water \(={10}^{3}\mathrm{kg}/{\mathrm{m}}^{3}\) )
[JEE Main 2025, 23 Jan (Shift 1)]
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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, 31 Jan (Shift 2)]
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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, 31 Jan (Shift 2)]
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A bubble of radius R is split into 27 drops of equal radius, and the work done is 10J. If the same bubble is split into 64 equal drops, the work done is:
(Shift 1 Memory Based)
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The surface tension of a soap bubble is \(0.03N/m\). The work done in increasing the diameter of bubble from 2 cm to 6 cm is \(\alpha \pi \times {10}^{-4}J\). The value of \(\alpha\) is ________ . (Take \(\pi =3.14\) )
[02 April, 2026 (Shift-2)]
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Pressure inside a soap bubble is greater than the pressure outside by an amount :
(given : \(R =\) Radius of bubble, \(S =\) Surface tension of bubble)
[JEE Main 2024, 6 Apr (Shift 2)]
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A spherical liquid drop of radius R acquires the terminal velocity \({v}_{1}\) when falls through a gas of viscosity \(\eta\). Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity \({v}_{2}\) falling through the same gas. The ratio of terminal velocities \({v}_{1}/{v}_{2}\) is ______.
[JEE Main 2026, 8 Apr (Shift 2)]
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Eight mercury drops, each of radius r, coalesce to form a bigger drop. The surface energy released in this process is (S = surface tension):
[JEE Main 2026, 5 Apr (Shift 2)]
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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, 28 Jan (Shift 1)]
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A sphere of mass \(M\) is dropped into glycerin. The density of glycerin is half the density of the sphere. After some time, the sphere moves down with constant velocity. What is the viscous force acting on the sphere?
(Shift II Memory Based)
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Two water drops each of radius '\(r\)' coalesce to from a bigger drop. If '\(T\)' is the surface tension, the surface energy released in this process is :
[JEE Main 2025, 2 Apr (Shift 2)]
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Find the pressure difference of an air bubble of radius 2 cm formed 20 cm below an open water surface and atmospheric pressure.
(Given surface tension of water = \(70\times 1{0}^{−3}\text{ }\text{N/m}\))(Shift - II Memory Based)
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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, 28 Jan (Shift 1)]
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A water spray gun is attached to a hose of cross sectional area 30 \({\mathrm{cm}}^{2}\). The gun comprises of 10 perforations each of cross sectional area of \(15{\mathrm{mm}}^{2}\). If the water flows in the hose with the speed of 50 \(\mathrm{cm}/\mathrm{s}\), calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)
[JEE Main 2026, 4 Apr (Shift 2)]
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A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is \(528{\mathrm{dm}}^{3}\) (dm : decimeter) The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm below the top of water level, then horizontal range of water falling on the ground in the beginning is _____ cm.
[JEE Main 2026, 6 Apr (Shift 2)]
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Statement 1: Surface tension of soap is greater than water.
Statement 2: Hot water flows faster than cold water.
(Shift I - Memory Based)
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Consider the following statements:
Statement 1: The surface tension of soap solution is greater than that of water.
Statement 2: Hot water flows faster than cold water.
Which of the following is correct?(shift 1 Memory based)
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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, 24 Jan (Shift 1)]
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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, 23 Jan (Shift 2)]
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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, 3 Apr (Shift 2)]
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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, 22 Jan (Shift 2)]
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An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density \(1000kg/{m}^{3}\). If the pressure inside the bubble is \(2100N/{m}^{2}\) greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use g\(=10m/{s}^{2}\))
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A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is \(\alpha \times {10}^{-6}J\). The value of \(\alpha\) is (Take surface tension of liquid \(=0.08N/m\) )
[JEE Main 2026, 2 Apr (Shift 1)]
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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)
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A horizontal pipe of variable cross-section has a fluid of density \(\rho\) flowing through it. At cross-sections A and B, the velocities are \({V}_{A}\) and \({V}_{B}\), and the pressures are \({P}_{A}\) and \({P}_{B}\). Find the correct relation between velocities.
(Shift - II Memory Based)
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Statement 1: Surface tension of soap is greater than water.
Statement 2: Hot water flows faster than cold water.
(Shift I - Memory Based)
Options are free to see. Unlock the correct answer and full explanation with Pass.
Pressure inside a soap bubble is greater than the pressure outside by an amount :
(given : \(R =\) Radius of bubble, \(S =\) Surface tension of bubble)
[JEE Main 2024, 6 Apr (Shift 2)]
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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 _____
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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:EndFragment
EndFragment
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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:EndFragment
EndFragment
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A bubble of radius R is split into 27 drops of equal radius, and the work done is 10J. If the same bubble is split into 64 equal drops, the work done is:
(Shift 1 Memory Based)
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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, 05 Apr (Shift 1)]
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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, 05 Apr (Shift 1)]
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Find the pressure difference of an air bubble of radius 2 cm formed 20 cm below an open water surface and atmospheric pressure.
(Given surface tension of water = \(70\times 1{0}^{−3}\text{ }\text{N/m}\))(Shift - II Memory Based)
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Two liquids A and B have \({\theta }_{\mathrm{A}}\) and \({\theta }_{\mathrm{B}}\) as contact angles in a capillary tube. If \(K=\cos {\theta }_{A}/\cos {\theta }_{B}\). then identify the correct statement:
[JEE Main 2025, 4 Apr (Shift 1)]
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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, 28 Jan (Shift 1)]
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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
Options are free to see. Unlock the correct answer and full explanation with Pass.
Consider the following statements:
Statement 1: The surface tension of soap solution is greater than that of water.
Statement 2: Hot water flows faster than cold water.
Which of the following is correct?(shift 1 Memory based)
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A hydraulic press can lift \(100 \mathrm{~kg}\) when a mass ' \(m\) ' is placed on the smaller piston. It can lift ________ \(\mathrm{kg}\) 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, 24 Feb (Shift 1)]
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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:
[Assume \(g=100 \mathrm{~m} / \mathrm{s}^{2}\) ]:
[JEE Main 2023, 8 Apr (Shift 2)]
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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 : [Use \(\pi=\frac{22}{7}\) ]
[JEE Main 2023, 29 Jan (Shift 1)]
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The pressure acting on a submarine is \(3 \times 10^{5} \mathrm{~Pa}\) at a certain depth. If the depth is doubled, the percentage in the pressure acting on the submarine would be:
(Assume that atmospheric pressure is \(1 \times 10^{5} \mathrm{~Pa}\) density of water is \(10^{3} \mathrm{kgm}^{-3}, g=10 \mathrm{~ms}^{-2}\) )
[JEE Main 2021, 16 Mar (Shift 1)]
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A mercury drop of radius \(10^{-3} \mathrm{~m}\) is broken into 125 equal size droplets. Surface tension of mercury is 0.45 Nm–1. The gain in surface energy nearly is:
[JEE Main 2023, 1 Feb (Shift 1)]
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When two soap bubbles of radii \(a\) and \(b(b>a)\) coalesce, the radius of curvature of common surface is:
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A raindrop with radius \(\mathrm{R}=0.2 \mathrm{~mm}\) falls from a cloud at a height \(h=2000 \mathrm{~m}\) above the ground. Assume that the drop is spherical throughout its fall and the force of buoyancy may be neglected, then the terminal speed attained by the raindrop is :
[Density of water \(f_{\mathrm{w}}=1000 \mathrm{kg m}^{-3}\) and Density of air \(f_{\mathrm{a}}=1.2 \mathrm{~kg m}^{-3}, g=10 \mathrm{~m} / \mathrm{s}^{2}\), Coefficient of viscosity of air \(\left.=1.8 \times 10^{-5} \mathrm{Nsm}^{-2}\right]\)
[JEE Main 2021, 27 July (Shift 2)]
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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason 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, 13 Apr (Shift 2)]
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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason 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, 6 Apr (Shift 2)]
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A leak proof cylinder of length \( 1 \mathrm{~m} \), made of a metal which has very low coefficient of expansion is floating vertically in water at \( 0^{\circ} \mathrm{C} \) such that its height above the water surface is \( 20 \mathrm{~cm} \). When the temperature of water is increased to \( 4^{\circ} \mathrm{C} \), the height of the cylinder above the water surface becomes \( 21 \mathrm{~cm} \). The density of water at \( \mathrm{T}=4^{\circ} \mathrm{C} \), relative to the density at \( \mathrm{T}=0^{\circ} \mathrm{C} \) is close to:
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The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, 5 cm. If the tube is dipped in a similar manner in another liquid B of surface tension and density double the values of liquid A, the height of liquid column raised in liquid B would be_____ m.
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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, 11 Apr (Shift 2)]
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Surface tension of a soap bubble is 2.0 × 10–2 Nm–1. Work done to increase the radius of soap bubble from 3.5 cm to 7cm will be:
\(\left[Take\pi =\frac{22}{7}\right]\)
[JEE Main 2023, 29 Jan (Shift 1)]
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An object is located at \(2 \mathrm{~km}\) beneath the surface of the water. If the fractional compression \(\frac{\Delta V}{V}\) is \(1.36 \%\), the ratio of hydraulic stress to the corresponding hydraulic strain will be [Given: density of water is \(1000 \mathrm{kgm}^{-3}\) and \(\left.\mathrm{g}=9.8 \mathrm{~ms}^{-2}.\right]\)
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If 1000 droplets of water of surface tension 0.07N/m, having same radius 1mm each, combine to form a single drop. In the process, the released surface energy is: (Take π = \(\frac{22}{7}\))
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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:
[Assume \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) ]:
[JEE Main 2023, 8 Apr (Shift 2)]
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If 1000 droplets of water of surface tension \(0.07 \mathrm{~N} / \mathrm{m}\) having same radius \(1 \mathrm{~mm}\) each, combine to form a single drop. In the process the released surface energy is:\(\left(\right.\) Take \(\left.\pi=\frac{22}{7}\right)\)
[JEE Main 2023, 31 Jan (Shift 1)]
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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, 10 Apr (Shift 1)]
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A raindrop with radius \(\mathrm{R}=0.2\mathrm{mm}\) falls from a cloud at a height \(h=2000 \mathrm{~m}\) above the ground. Assume that the drop is spherical through its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is :
[Density of water \(f_{\mathrm{w}}=1000 \mathrm{kg m}^{-3}\) and Density of air \(f_{\mathrm{a}}=1.2 \mathrm{~kg}^{-3}, g=10 \mathrm{~m} / \mathrm{s}^{2}\), Coefficient of viscosity of air \(\left.=1.8 \times 10^{-5} \mathrm{Nsm}^{-2}\right]\)
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A barometer is constructed using a liquid(density\(=760\mathrm{kg}/{\mathrm{m}}^{3}\)). What would be the height of the liquid column, when a mercury barometer reads \(76\mathrm{cm}\)? (density of mercury \(=13600\mathrm{kg}/{\mathrm{m}}^{3}\))
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A mercury drop of radius \( 10^{-3} \mathrm{~m} \) is broken into \( 125 \)
equal size droplets. Surface tension of mercury is
\( 0.45 \mathrm{~N} \mathrm{~m}^{-1} \). The gain in surface energy is:
[JEE Main 2023, 1 Feb (Shift 1)]
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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 B of surface tension and density double the values of liquid \(A\), the height of liquid column raised in liquid \(B\) would be ...... m.
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