Q 11-10-100JEE MainJEE Main 2020 (7 Jan, Shift 1)Easy
A non-isotropic solid metal cube has coefficients of linear expansion of $5\times10^{-5}\ /^\circ\text{C}$ along the $x$-axis and $5\times10^{-6}\ /^\circ\text{C}$ along the $y$ and $z$-axes. If the coefficient of volume expansion of the solid is $C\times10^{-6}\ /^\circ\text{C}$, then the value of $C$ is ______.
Numerical value type. Enter your answer.
Answer: 60
$V = xyz$, so the fractional volume change is the sum of the fractional length changes:
$$\gamma = \alpha_x + \alpha_y + \alpha_z = 50\times10^{-6} + 5\times10^{-6} + 5\times10^{-6} = 60\times10^{-6}\ /^\circ\text{C}$$
So $C = 60$.
Solution by Sreeraj P, M.Sc Physics