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

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

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

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

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

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Solution

The correct option is A $\frac{f_{1} - f_{2}}{f_{2} t_{1} - f_{1} t_{2}}$
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 $= V_{0} (1 + γ t_{1})$ .....(i)
and fraction of solid submerged at $t_{2}^{\circ} = f_{2}$ . Volume of displaced liquid $= V_{0} (1 + γ t_{2})$ .....(ii)
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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