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