A wooden ball of density D is immersed in water of density d to a depth h//2 below the surface of water and then relased. To what height will the ball jump out of water ?

Options

A. `(d)/(D)h`
B. `((d)/(D)-1)h`
C. `h`
D. Zero

Answer

B

Explanation

Let the volumee of the ball be V.
Force on the ball due to upthrust`=Vdg`
Net upward force=Vdg-VDg
If upward acceleration is a, then
`VD a=V dg-VD g`
`impliesa=((d-D)/(D))g`
Velocity on reaching the surface,
`v=sqrt(2ah)`
Further, `v=sqrt(2gH)`
`therefore2ah=2gH` or
`H=(ah)/(g)=((d-D)/(D))h=(((d)/(D)-1)h`