A body is floating in a liquid. At two temperatures $t_{1}^{\circ} C$ and $t_{2}^{\circ} C$ of the liquid, fractions $f_{1}$ and $f_{2}$ of the volumes of the body remain immersed in the liquid. Coefficient of volume expansion of the liquid is:

\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 $\frac{f_{1} - f_{2}}{f_{2} t_{1} - f_{1} t_{2}}$
The fraction of a body immersed in a liquid is given by the formula,

$f = \frac{ρ_{b}}{ρ_{l}}$

Hence, $f_{1} = \frac{ρ_{b}}{ρ_{l}} (1 + γ t_{1})$ and $f_{2} = \frac{ρ_{b}}{ρ_{l}} (1 + γ t_{2})$ where, $γ$ is the coefficient of volume expansion of liquid.

Dividing the above two equations, we get

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

Thus, $γ = \frac{f_{1} - f_{2}}{f_{2} t_{1} - f_{1} t_{2}}$

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