Q 11-10-001NEETNEET 2026Top questionEasy
The temperature of a metallic sphere of radius $R$ is increased by a small amount $\Delta T$. If the linear coefficient of thermal expansion of the metal is $\alpha$, the approximate increase in the volume of the sphere is :
Answer: (C) $4\pi R^3 \alpha \Delta T$
Concept. For a small temperature rise $\Delta V = \gamma V\Delta T$, with volume coefficient $\gamma = 3\alpha$.
Step 1. Substitute. $V = \dfrac43\pi R^3$:
$$\Delta V = 3\alpha \cdot \frac43\pi R^3 \cdot \Delta T = 4\pi R^3\alpha\Delta T$$
Answer. $4\pi R^3\alpha\Delta T$ (Option C).
Solution by Sreeraj P, M.Sc Physics