Question

When a block of iron floats in mercury at $0^{\circ }C$, a fraction $k_1$ of its volume submerged, while at the temperature ${60}^{\circ }C$, a fraction $k_2$ is keen to be submerged the coefficient of volume expansion of iron of $g_{Fe}$ and that of mercury is $g_{Hg}$, then the ratio $\frac{k_1}{k_2}$ can be expressed as

• A. $\frac{1+60{\gamma }_{Fe}}{1+60{\gamma }_{Hg}}$
• B. $\frac{1-60{\gamma }_{Fe}}{1+60{\gamma }_{Hg}}$
• C. $\frac{1+60{\gamma }_{Fe}}{1-60{\gamma }_{Hg}}$
• D. $\frac{1+60{\gamma }_{Hg}}{1+60{\gamma }_{Fe}}$

Answer 1

The correct option is A $\frac{1+60{\gamma }_{Fe}}{1+60{\gamma }_{Hg}}$

$k_1=\frac{(d_{fe}{)}_0}{(d_{Hg}{)}_0}{k}_2=\frac{(d_{Fe}{)}_{{60}^{\circ }}}{(d_{Hg}{)}_{{60}^{\circ }}}=\frac{\frac{(dFe{)}_0}{1+{\gamma }_{Fe}60}}{\frac{(d_{Hg}{)}_0}{1+{\gamma }_{Hg}60}}\therefore \frac{k_1}{k_2}=\frac{1+60{\gamma }_{Fe}}{1+60{\gamma }_{Hg}}$