When a liquid in a glass vessel is heated, its apparent expansion is $10.30 \times 10^{-4}\ °\text{C}^{-1}$. When the same liquid is heated in a metallic vessel, its apparent expansion is $10.06 \times 10^{-4}\ °\text{C}^{-1}$. The coefficient of linear expansion of the metal is ($\alpha_{glass} = 9 \times 10^{-6}\ °\text{C}^{-1}$)
Answer: (D) $17 \times 10^{-6}\ °\text{C}^{-1}$
Concept. Real expansion $=$ apparent expansion $+$ expansion of the vessel ($3\alpha$). The real coefficient of the liquid is the same in both vessels.
Step 1. Real coefficient (glass vessel).
$$\gamma_R = 10.30 \times 10^{-4} + 3 \times 9 \times 10^{-6} = 10.57 \times 10^{-4}\ °\text{C}^{-1}$$
Step 2. Metal vessel.
$$\gamma_{\text{metal}} = 10.57 \times 10^{-4} - 10.06 \times 10^{-4} = 51 \times 10^{-6}\ °\text{C}^{-1}$$
Step 3. Linear coefficient. $\alpha_{\text{metal}} = \dfrac{51 \times 10^{-6}}{3} = 17 \times 10^{-6}\ °\text{C}^{-1}$.
Answer. $17 \times 10^{-6}\ °\text{C}^{-1}$ (Option D).
Solution by Sreeraj P, M.Sc Physics