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When a block of iron floats in mercury at $0^{\circ} C,$ a fraction of $k_{1}$ of its volume is submerged, while at temp $60^{\circ} C,$ a fraction of $k_{2}$ is seen to be submerged. If the coefficient of volume expansion of iron is $γ_{F e}$ and that of mercury is $γ_{H g}$ . Then the ratio of $\frac{k_{1}}{k_{2}}$ can be expressed as.

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$\frac{1 - 60 γ_{F e}}{1 + 60 γ_{H g}}$

$\frac{1 + 60 γ_{H g}}{1 + 60 γ_{F e}}$

$\frac{1 + 60 γ_{F e}}{1 - 60 γ_{H g}}$

$\frac{1 + 60 γ_{F e}}{1 + 60 γ_{H g}}$

answer is A.

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Detailed Solution

$f_{i n} = \frac{d_{B}}{d_{l}} \to \frac{f_{1}}{f_{2}} = \frac{d_{B_{1}}}{d_{B_{2}}} \frac{d_{l_{2}}}{d_{l_{1}}} = \frac{1 + 60 γ_{F e}}{1 + 60 γ_{H g}}$

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