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Q.

In an experiment to verify Stokes law, a small spherical ball of radius r and density ρ 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)

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a

r4

b

r2

c

r3

d

r

answer is A.

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Detailed Solution

Velocity of the ball after free fall :  V=2gh given it is equivalent to terminal velocity in a liquidmg−B=Fdrag​⇒ρ43πr3g−J43πr3g=6πηrVT⇒ρ−J43πr2g=6πη2gh​⇒h ∝ r4
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