Q 11-06-146JEE MainJEE Main 2021 (27 Jul, Shift 2)Easy
In the given figure, two wheels $P$ and $Q$ are connected by a belt $B$. The radius of $P$ is three times that of $Q$. In the case of the same rotational kinetic energy, the ratio of rotational inertias $\left(\dfrac{I_1}{I_2}\right)$ will be $x : 1$. The value of $x$ will be ______.
Numerical value type. Enter your answer.
Answer: 9
The belt does not slip, so the rim speeds are equal: $\omega_1(3R) = \omega_2R \Rightarrow \omega_2 = 3\omega_1$.
Equal kinetic energy: $\dfrac12I_1\omega_1^2 = \dfrac12I_2\omega_2^2$
$$\frac{I_1}{I_2} = \left(\frac{\omega_2}{\omega_1}\right)^2 = 9$$
Solution by Sreeraj P, M.Sc Physics