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Q.

A jar is filled with two non-mixing liquids 1 and 2 having densities ρ1 and ρ2 respectively. A solid ball, made of a material of density ρ3 , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ρ1,ρ2 and ρ3 ?
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a

ρ1>ρ3>ρ2

b

ρ1<ρ2<ρ3

c

ρ3<ρ1<ρ2

d

ρ1<ρ3<ρ2

answer is D.

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Detailed Solution

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As liquid 1 floats over liquid 2. The lighter liquid floats over heavier liquid. So, ρ1<ρ2
Also ρ3<ρ2 because the ball of density ρ3 does not sink to the bottom of the jar.
Also ρ3>ρ1 otherwise the ball would have floated in liquid 1. We conclude that
ρ1<ρ3<ρ2.

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