JEE MAIN - Physics (2008 - No. 20)
A jar is filled with two non-mixing liquids $$1$$ and $$2$$ having densities $${\rho _1}$$ and $${\rho _2}$$ respectively. A solid ball, made of a material of density $${\rho _3}$$, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $${\rho _1}$$ , $${\rho _1}$$ and $${\rho _3}$$ ?
$${\rho _3} < {\rho _1} < \rho {}_2$$
$${\rho _1} > {\rho _3} > \rho {}_2$$
$${\rho _1} < {\rho _2} < \rho {}_3$$
$${\rho _1} < {\rho _3} < \rho {}_2$$
Explanation
From the figure it is clear that liquid $$1$$ floats on liquid $$2.$$ The lighter liquid floats over heavier liquid. Therefore we can conclude that $${\rho _1} < {\rho _2}$$
Also $${\rho _3} < {\rho _2}$$ otherwise the ball would have sink to the bottom of the jar.
Also $${\rho _3} > {\rho _1}$$ otherwise the ball would have floated in liquid $$1.$$ From the above discussion we conclude that $${\rho _1} < {\rho _2} < {\rho _3}.$$
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