Q 11-06-107JEE MainJEE Main 2023 (31 Jan, Shift 2)Medium
Two discs of same mass and different radii are made of different materials such that their thicknesses are $1\ \text{cm}$ and $0.5\ \text{cm}$ respectively. The densities of materials are in the ratio $3:5$. The moment of inertia of these discs respectively about their diameters will be in the ratio of $\dfrac x6$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 5
Equal masses: $\rho_1\pi r_1^2t_1=\rho_2\pi r_2^2t_2$, so
$$\frac{r_1^2}{r_2^2}=\frac{\rho_2t_2}{\rho_1t_1}=\frac{5\times0.5}{3\times1}=\frac56$$
About a diameter $I=\dfrac{mr^2}{4}$, so $\dfrac{I_1}{I_2}=\dfrac{r_1^2}{r_2^2}=\dfrac56$ and $x=5$.
Solution by Sreeraj P, M.Sc Physics