Question

A cube of iron whose sides are of length $L$, is floating in a beaker containing mercury. The weight of iron cube is $W$. The density of iron is ${\rho }_I$ and that of mercury is ${\rho }_M$. The depth to which the cube sinks is given by the expression

• A. $W{L}^2{\rho }_I$
• B. $W{L}^2{\rho }_M$
• C. $\frac{W}{L^2{\rho }_I}$
• D. $\frac{W}{L^2{\rho }_{M}g}$

Answer 1

The correct option is D $\frac{W}{L^2{\rho }_{M}g}$

Let $h$ be height of iron cube inside the mercury.
At equilibrium position, $W=F_B$
From Archimedes principle, $F_B={\rho }_{M}Vg={\rho }_M{L}^{2}hg$
$\Rightarrow W={\rho }_M{L}^{2}hg$
$\Rightarrow h=\frac{W}{L^2{\rho }_{M}g}$