Q 11-06-121JEE MainJEE Main 2023 (13 Apr, Shift 1)Medium
A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $\pi:22$, then the value of its angular speed will be ______ $\text{rad s}^{-1}$.
Numerical value type. Enter your answer.
Answer: 4
$L=\tfrac25mR^2\omega$, $E=\tfrac7{10}mR^2\omega^2$, so $\dfrac LE=\dfrac{4}{7\omega}=\dfrac{\pi}{22}$.
$$\omega=\frac{88}{7\pi}=\frac{88}{22}=4\ \text{rad s}^{-1}\quad\left(\pi=\tfrac{22}{7}\right)$$
Solution by Sreeraj P, M.Sc Physics