Q 11-10-021JEE MainEAMCET 2011 (Engineering)Medium
A non-conducting body floats in a liquid at $20°$C with $\dfrac{2}{3}$ of its volume immersed in the liquid. When the liquid temperature is increased to $100°$C, $\dfrac{3}{4}$ of the body's volume is immersed. The coefficient of real expansion of the liquid is (neglecting the expansion of the container of the liquid)
Answer: (B) $15.6 \times 10^{-4}\ °\text{C}^{-1}$
Floating: $f\rho$ is constant, so $\dfrac{\rho_{20}}{\rho_{100}} = \dfrac{f_{100}}{f_{20}} = \dfrac{3/4}{2/3} = \dfrac{9}{8}$.
$\dfrac{\rho_{20}}{\rho_{100}} = 1 + \gamma(80)$:
$$\gamma = \frac{1/8}{80} = 1.56 \times 10^{-3} = 15.6 \times 10^{-4}\ °\text{C}^{-1}$$
Solution by Sreeraj P, M.Sc Physics