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 \(.....\, .\)

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Answer & Solution

Correct Answer

(C) \(9\)

Detailed explanation

\(\frac{1}{2} I_{1}\left(\omega_{1}\right)^{2}=\frac{1}{2} I_{2}\left(\omega_{2}\right)^{2}\)

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

\(\frac{I_{1}}{I_{2}}=\frac{9}{1}\)

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