In the given figure, two wheels P and Q are connected by a belt B ....

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 ______.

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

Correct answer

Step-by-step solution

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

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

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

$\dfrac{{I}_{1}}{{I}_{2}} = \dfrac{9}{1}$

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