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Question

# A container of a large uniform cross-sectional area A resting on a horizontal surface holds two immiscible, non-viscous and incompressible liquids of densities d and 2d, each of height H2 as shown in figure. The lower denisty liquid is open to the atomsphere. A homogenous solid cylinder of length L(L<H2), cross-sectional area A5 is immersed such that it floats with its axis vertical to the liquid-liquid interface with length L4 in the denser liquid. The density of the solid is

A
3d2
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B
4d3
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C
5d4
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D
3d
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Solution

## The correct option is C 5d4Let the density of the solid sylinder be D. Mass of solid cylinder = cross-sectional area × length × density ⇒M=A5×L×D=15ALD ∴ Weight of solid cylinder W=15ALDg Buoyant force acting on the cylinder FB = weight of denser liquid displaced + weight of lighter liquid displaced. FB=A5×L4×2d×g+A5×3L4×d×g ⇒FB=(110+320)ALdg ⇒FB=14ALdg From the principle of floatation , W=FB ⇒15ALDG=14ALdg ∴D=5d4 Hence, option (c) is the correct answer.

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