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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−ρη g

b

281r2ρ−1η g

c

281r4ρ−1η2g

d

29r4ρ−1η2g

answer is C.

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Detailed Solution

Velocity of ball when it strikes the water surface v=2gh …(i)Terminal velocity of ball inside the water v=29r2gρ−1η …(ii)Equating (i) and (ii) we get 2gh=29r2gη(ρ−1)⇒h=281r4ρ−1η2g

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