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A ball of radius r and density ρ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is η, the value of h is given by

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a

29r21−ρηg

b

281r2ρ−1ηg

c

281r4ρ−1η2g

d

29r4ρ−1η2g

answer is C.

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Detailed Solution

Velocity of ball when it strikes the water surfacev=2gh.......(i)Terminal velocity of ball inside the waterv=29r2g(ρ−1)η........(ii)Equating (i) and (ii), we get 2gh=29r2gη(ρ−1)⇒h=281r4ρ−1η2g
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