Q 11-06-060JEE MainJEE Main 2026 (24 Jan, Shift 2)Easy
A uniform solid cylinder of length $L$ and radius $R$ has moment of inertia about its axis equal to $I_1$. A small co-centric cylinder of length $L/2$ and radius $R/3$ carved from this cylinder has moment of inertia about its axis equals to $I_2$. The ratio $I_1/I_2$ is ______ .
Numerical value type. Enter your answer.
Answer: 162
Mass $\propto$ volume $\propto LR^2$. The small cylinder has mass
$$m = M\times\frac12\times\frac19 = \frac M{18}$$
$$I_1 = \frac12MR^2,\qquad I_2 = \frac12\cdot\frac M{18}\cdot\frac{R^2}{9} = \frac{MR^2}{324}$$
$$\frac{I_1}{I_2} = \frac{1/2}{1/324} = 162$$
Solution by Sreeraj P, M.Sc Physics