Q 11-10-016JEE MainEAMCET 2012 (Medical)Hard
A solid whose volume does not change with temperature floats in a liquid. At temperatures $t_1$ and $t_2$ of the liquid, the fractions of the volume of the solid that remain submerged are $f_1$ and $f_2$ respectively. The coefficient of absolute expansion of the liquid is
Answer: (B) $\dfrac{f_1 - f_2}{f_2t_1 - f_1t_2}$
The buoyant force always equals the (constant) weight, so the displaced volume times the liquid density is constant: $f\rho = $ constant. With $\rho = \dfrac{\rho_0}{1 + \gamma t}$:
$$\frac{f_1}{1 + \gamma t_1} = \frac{f_2}{1 + \gamma t_2} \;\Rightarrow\; f_1 + f_1\gamma t_2 = f_2 + f_2\gamma t_1$$
$$\gamma = \frac{f_1 - f_2}{f_2t_1 - f_1t_2}$$
Solution by Sreeraj P, M.Sc Physics