Q 11-10-078JEE MainJEE Main 2022 (25 Jun, Shift 2)Medium
A solid metallic cube having total surface area $24\ \text{m}^2$ is uniformly heated. If its temperature is increased by $10^\circ\text{C}$, calculate the increase in volume of the cube. (Given $\alpha = 5.0\times10^{-4}\ ^\circ\text{C}^{-1}$)
Answer: (B) $1.2\times10^5\ \text{cm}^3$
$6a^2 = 24\Rightarrow a = 2\ \text{m}$, so $V = 8\ \text{m}^3$. Volume expansion coefficient $\gamma = 3\alpha = 1.5\times10^{-3}\ ^\circ\text{C}^{-1}$.
$$\Delta V = V\gamma\Delta T = 8\times1.5\times10^{-3}\times10 = 0.12\ \text{m}^3 = 1.2\times10^5\ \text{cm}^3$$
Solution by Sreeraj P, M.Sc Physics