When a block of iron floats in mercury at 0°C, a fraction $k_1$ of its volume is submerged, while at the temperature 60°C, a fraction $k_2$ is seen to be submerged. If the coefficient of volume expansion of iron is ${\gamma }_{\mathrm{Fe}}$ and that  of mercury is ${\gamma }_{\mathrm{Hg}},$ then the ratio $k_1/k_2$ can be expressed as

Let $V_0$ be the total volume of the block of iron at 0°C and V its total volume at 60°C. Then 

$V=V_0\left(1+60{\gamma }_{\mathrm{Fe}}\right)$

Let  $V_0$ be the volume of the block submerged in mercury at 0°C and v the volume submerged at 60°C. Then 

$\mathrm{v}={\mathrm{v}}_0\left(1+60{\gamma }_{\mathrm{Hg}}\right)$

Dividing (1) by (2), we have

$\frac{V/v}{V_0/v_0}=\frac{1+60{\gamma }_{\mathrm{Fe}}}{1+60{\gamma }_{\mathrm{Hg}}}$

Given $\frac{v_0}{V_0}=k_1\text{ and }\frac{v}{V}=k_2$ Using these in (3), we find

that the correct choice is (1)