Q.

A small ball of density ρ  is immersed in a liquid of density σ(σ>ρ)  to a depth h and then released. The highest above the surface of water up to which the ball will jump is

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a

σhρ

b

(σρ−1)h

c

(1−ρσ)h

d

ρhσ

answer is B.

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Detailed Solution

Acceleration a=Fnetm=upthrust - mgm=Vσg−VρgVρ=σ−ρρg Velocity on reaching the surfaceu=2(σ−ρ)ρghHeight attained above the surface is h'=u22g⇒  h'=2(σ−ρρ)gh.12g⇒  h'=(σ−ρρ)h
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