Q 11-10-011JEE MainEAMCET 2012 (Engineering)Easy
When the temperature of a body increases from $t$ to $t + \Delta t$, its moment of inertia increases from $I$ to $I + \Delta I$. The coefficient of linear expansion of the body is $\alpha$. The ratio $\dfrac{\Delta I}{I}$ is
Answer: (D) $2\alpha\Delta t$
Concept. $I \propto$ (mass) $\times$ (length)$^2$. The mass is unchanged and every length grows by the factor $(1 + \alpha\Delta t)$.
Step 1. New moment of inertia.
$$I + \Delta I = I(1 + \alpha\Delta t)^2 \approx I(1 + 2\alpha\Delta t)$$
Step 2. Ratio. $\dfrac{\Delta I}{I} = 2\alpha\Delta t$.
Answer. $2\alpha\Delta t$ (Option D).
Solution by Sreeraj P, M.Sc Physics