Question 52 of 280

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 ______.

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Answer: 9

$\dfrac{1}{2}{I}_{1}{\left({\omega }_{1}\right)}^{2}=\dfrac{1}{2}{I}_{2}{\left({\omega }_{2}\right)}^{2}$
${I}_{1}{\left(\dfrac{v}{3R}\right)}^{2}={I}_{2}{\left(\dfrac{v}{R}\right)}^{2}$
$\dfrac{{I}_{1}}{{I}_{2}}=\dfrac{9}{1}$