Question

In the given figure, two wheels $P$ and $Q$ are connected by a belt $B$. The radius of $P$ is three times as that of $Q$. In case of same rotational kinetic energy, the ratio of rotational inertias $\left(\frac{I_{1}}{I_{2}}\right)$ will be $x: 1$. The value of $x$ will be____

Answer 1

$\frac{1}{2} I_{1}\left(\omega_{1}\right)^{2}=\frac{1}{2} I_{2}\left(\omega_{2}\right)^{2}$
$I_{1}\left(\frac{v}{3 R}\right)^{2}=I_{2}\left(\frac{v}{R}\right)^{2}$
$\frac{I_{1}}{I_{2}}=\frac{9}{1}$