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) $15.6 \times 10^{-4}\ °\text{C}^{-1}$
Concept. For a floating body, (fraction immersed) $\times$ (liquid density) is constant; and $\dfrac{\rho_{20}}{\rho_{100}} = 1 + \gamma\Delta T$.
Step 1. Density ratio.
$$\frac{\rho_{20}}{\rho_{100}} = \frac{f_{100}}{f_{20}} = \frac{3/4}{2/3} = \frac98$$
Step 2. Coefficient.
$$1 + 80\gamma = \frac98 \;\Rightarrow\; \gamma = \frac{1/8}{80} = 1.56 \times 10^{-3} = 15.6 \times 10^{-4}\ °\text{C}^{-1}$$
Answer. $15.6 \times 10^{-4}\ °\text{C}^{-1}$ (Option B).
Solution by Sreeraj P, M.Sc Physics