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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Solution

The correct option is A
As with the rise in temperature, the liquid undergoes volume expansion therefore the fraction of solid submerged in liquid increases.
Fraction of solid submerged at ${t_{1}}^{\circ} C = f_{1}$ = Volume of displaced liquid $= V_{0} (1 + γ t_{1}) \dots \dots (i)$ and fraction of solid submerged at ${t_{2}}^{\circ} C = f_{2}$ = Volume of displaced liquid $= V_{0} (1 + γ t_{2}) \dots \dots (i i)$
From (i) and (ii) $\frac{f_{1}}{f_{2}} = \frac{1 + γ t_{1}}{1 + γ t_{2}}$ $\Rightarrow$ $γ = \frac{f_{1} - f_{2}}{f_{2} t_{1} - f_{1} t_{2}}$

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