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A solid whose volume does not change with temperature floats in a liquid. For two different temperatures $t_{1}$ and $t_{2}$ of the liquid, fractions $f_{1}$ and $f_{2}$ of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to

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$\frac{f_{1} + f_{2}}{f_{2} t_{1} + f_{1} t_{2}}$

$\frac{f_{1} + f_{2}}{f_{1} t_{1} + f_{2} t_{2}}$

$\frac{f_{1} - f_{2}}{f_{1} t_{1} - f_{2} t_{2}}$

$\frac{f_{1} - f_{2}}{f_{2} t_{1} - f_{1} t_{2}}$

answer is A.

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Detailed Solution

Fraction of solid submerged at $t_{1} ° c =$ volume of displaced liquid $f_{1} = V_{0} (1 + γ t_{1})$

Fraction of solid submerged at $t_{2} ° c =$ volume of displaced liquid $f_{2} = V_{0} (1 + γ t_{2})$

$\frac{f_{1}}{f_{2}} = \frac{1 + γ t_{1}}{1 + γ t_{2}} \Rightarrow γ = \frac{f_{1} - f_{2}}{f_{2} t_{1} - f_{1} t_{2}}$

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