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Question

A wooden ball of density D is immersed in water of density d to a depth h below the surface of water and then released. Upto what height will the ball jump out of water( measured from surface of water) ?

A
dDh
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B
(dD1)h
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C
h
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D
Zero
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Solution

The correct option is B (dD1)h
Let the volume of the ball be V.
Force on the ball due to upthrust =Vdg
Net upward force =VdgVDg
upward acceleration is given by
VDa=VdgVDg
a=(dDD)g
Velocity on reaching the surface, v=2ah
When ball leaves the surface, let maximum height reached be H.
Then,
v=2gH
H=ahg=(dDD)h=(dD1)h
Hence, the correct answer is option (b).

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