Q.

In the Figure shown, the heavy cylinder (radius R) resting on a smooth surface separates two liquids of densities 2ρ and 3ρ. The height h for the equilibrium of cylinder must be

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a

3R2

b

R32

c

R2

d

R23

answer is B.

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Detailed Solution

Torque due to hydrostatic force about centre of sphere is zero because hydrostatic force passes through the centre. So, horizontal force on the cylinder due to two liquids must cancel out.⇒ FLHS=FRHSIf L be the length of cylinder, thenPavg left hL=Pavg right RL⇒12(2ρgh)(hL)=12(3ρgR)(RL)⇒h=32R
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In the Figure shown, the heavy cylinder (radius R) resting on a smooth surface separates two liquids of densities 2ρ and 3ρ. The height h for the equilibrium of cylinder must be