A small spherical ball of radius \(0.1\) mm and density \(10^{4}\) kg-m–3 falls freely under gravity through a distance of \(h\) before entering a tank of water. If after entering the water, the velocity of the ball does not change and it continues to fall with the same constant velocity inside water, then the value of \(h\) will be:
(Given \(g=10\) ms–2, viscosity of water \(=1.0\times10^{-5}\) N-sm–2)
1. \(15\) m
2. \(25\) m
3. \(20\) m
4. \(10\) m
Subtopic:  Stokes' Law |
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A wooden sphere is at rest at the bottom of a lake. When it is released then it will: (Consider viscous effects)
1. move up with constant acceleration.
2. move up with constant velocity.
3. move up with variable acceleration and finally, it may attain a terminal speed.
4. remain at rest.
Subtopic:  Stokes' Law |
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The terminal velocity \((v_{T})\) of the spherical raindrop depends on the radius \((r)\) of the spherical raindrop as: 
1. \(r^{1/2}\)
2. \(r\) 
3. \(r^{2}\)
4. \(r^{3}\)
Subtopic:  Stokes' Law |
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The viscous drag acting on a metal sphere of diameter \(1\) mm, falling through a fluid of viscosity \(0.8\) Pa-s with a velocity of \(2\) m s–1 is nearly equal to:
1. \(15\times 10^{-3}~\text{N}\)
2. \(30\times 10^{-3}~\text{N}\)
3. \(1.5\times 10^{-3}~\text{N}\)
4. \(20\times 10^{-3}~\text{N}\)
Subtopic:  Stokes' Law |
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NEET - 2023
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The diameter of an air bubble which was initially \(2\) mm, rises steadily through a solution of density \(1750\) kgm–3 at the rate of \(0.35\) cms–1. The coefficient of viscosity of the solution is (in the nearest integer):
(The density of air is negligible).
1. \(15\) poise
2. \(9\) poise
3. \(18\) poise
4. \(11\) poise
Subtopic:  Stokes' Law |
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The terminal velocity of a copper ball of radius \(5~\text{mm}\) falling through a tank of oil at room temperature is \(10~\text{cm}~\text{s}^{-1}\) . If the viscosity of oil at room temperature is \(0.9~\text{kg}~\text{m}^{-1}~\text{s}^{-1}\), the viscous drag force is:
1. \(8.48 \times10^{-3}\) N
2. \(8.48 \times10^{-5}\) N
3. \(4.23 \times10^{-3}\) N
4. \(4.23 \times10^{-6}\) N
Subtopic:  Stokes' Law |
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NEET - 2022
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A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. The plot shown in the figure indicates the one that represents the velocity \((v)\) of the pebble as a function of time \((t).\)

1. 2.
3. 4.
Subtopic:  Stokes' Law |
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In Millikan’s oil drop experiment, what is the terminal speed of an uncharged drop of radius \(2\times10^{-5}\) m and density \(1.2\times10^{3}\) kg-m–3? (Take the viscosity of air at the temperature of the experiment to be \(1.8\times10^{-5}\) Pa-s.)

1. \(2.7\) cm/s 2. \(3.9\) cm/s
3. \(5.8\) cm/s 4. \(4.6\) cm/s
Subtopic:  Stokes' Law |
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Spherical balls of radius \(R\) are falling in a viscous fluid of viscosity η with a velocity \(v.\) The retarding viscous force acting on the spherical ball is:

1. directly proportional to \(R\) but inversely proportional to \(v.\)
2. directly proportional to both radius \(R\) and velocity \(v.\)
3. inversely proportional to both radius \(R\) and velocity \(v.\)
4. inversely proportional to \(R\) but directly proportional to velocity \(v.\)

Subtopic:  Stokes' Law |
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A particle released from rest is falling through a thick fluid under gravity. The fluid exerts a resistive force on the particle proportional to the square of its speed. Which one of the following graphs best depicts the variation of its speed \(v\) with time \(t?\)

1.   2.
3. 4.
Subtopic:  Stokes' Law |
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