A wooden ball of density p is dropped from rest from a height 'h' into the lake of water density `sigma (sigma > p)`. Neglecting viscosity, the maximum depth to which the body sinks before returning to float is :

Options

A. `(hp)/(p-sigma)`
B. `(h(p-sigma))/p`
C. `(h(sigma-p))/(sigma)`
D. `(hp)/(sigma-p)`

Answer

D

Explanation

Here P.E. of the ball
mgh`=[m/pxxsigmaxxg-mg]`H, where His the depth to which it sinks. Then
`h=[(sigma)/p-1]`H or H`=(ph)/(sigma-p)`
Correct choice is (d).