When a block of iron floats in mercury at $0^{0} C$ , a fraction $K_{1}$ of its volume is submerged, while at the temperature $60^{0} C$ , a fraction $K_{2}$ 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 $\frac{K_{1}}{K_{2}}$ can be expressed as

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

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

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

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

answer is A.

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