A ball of radius r and density r 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 `eta` the value of h is given by
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Options

A. `2/9 r^2 ((1-rho)/(eta))g`
B. `2/81 r^2 ((rho-1)/(eta))g`
C. `2/81 r^4 ((rho-1)/(eta))^2 g`
D. `2/9 r^4 ((rho-1)/(eta))^2g`

Answer

C

Explanation

Velocity before entering the water -
`v=sqrt(2gh)`
`v_T=2/9 r^2 g(rho-1)/(eta)`
`sqrt(2gh)= 2/9 (r^2 g)/(eta) (rho-1) implies h=(2)/(81) r^4((rho-1)/(eta))^2 g`