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A jar 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 $\rho_1, \rho_2$ and $\rho_3$ ?

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Verified Answer
The correct answer is:
$\rho_1 < \rho_3 < \rho_2$
$\rho_1 < \rho_3 < \rho_2$
As liquid 1 floats above liquid 2 ,
$$
\rho_1 < \rho_2
$$
The ball is unable to sink into liquid 2 ,
$\rho_3 < \rho_2$ The ball is unable to rise over liquid 1 ,
$\begin{array}{ll} & \rho_1 < \rho_3 \\ \text { Thus, } & \rho_1 < \rho_3 < \rho_2\end{array}$
$$
\rho_1 < \rho_2
$$
The ball is unable to sink into liquid 2 ,
$\rho_3 < \rho_2$ The ball is unable to rise over liquid 1 ,
$\begin{array}{ll} & \rho_1 < \rho_3 \\ \text { Thus, } & \rho_1 < \rho_3 < \rho_2\end{array}$
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