Q 11-06-197JEE MainJEE Main 2020 (4 Sep, Shift 2)Easy
Consider two uniform discs of the same thickness and different radii $R_1 = R$ and $R_2 = \alpha R$ made of the same material. If the ratio of their moments of inertia $I_1$ and $I_2$, respectively, about their axes is $I_1 : I_2 = 1 : 16$ then the value of $\alpha$ is:
Answer: (C) $2$
Same thickness and material: $M \propto R^{2}$, so $I = \tfrac12MR^{2} \propto R^{4}$.
$$\frac{I_1}{I_2} = \frac{1}{\alpha^{4}} = \frac1{16} \Rightarrow \alpha = 2$$
Solution by Sreeraj P, M.Sc Physics