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  4. The relation between length L and radius R of the cylinder, if its moment of inertia about its axis is equal to that about the equatorial axis, will be

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Q. The relation between length $L$ and radius $R$ of the cylinder, if its moment of inertia about its axis is equal to that about the equatorial axis, will be

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

$\frac{m R^{2}}{2}=M\left(\frac{L^{2}}{12} + \frac{R^{2}}{4}\right)$
or $\frac{R^{2}}{2}=\frac{L^{2}}{12}+\frac{R^{2}}{4}$
or $L=\sqrt{3}R$