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Q.

A wooden ball of density ρ is immersed in water of density ρ0 to depth h and then released. The height H above the surface of water upto which the ball jump out of water is

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a

zero

b

h

c

ρ0hρ

d

ρ0ρ−1h

answer is D.

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Detailed Solution

Let V be the volume of wooden ball. The mass of ball is m = Vρ.Upward acceleration,          a= upward thrust-weight of ball  mass of ball ⇒ a=Vρ0g−VρgVρ=ρ0−ρgρIf v' is the velocity of ball on reaching the surface after being released at depth hisv=2as=2p0−ρρgh1/2If H is the vertical distance reached by ball above the surface of water, thenH=v22g=2ρ0−ρρgh×12g=ρ0−ρρh=ρ0ρ−1h
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