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(D) The kinetic energy of rotation $K$ is related to angular momentum $L$ and moment of inertia $I$ by the formula $K = \frac{L^2}{2I}$.Rearranging fo

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$1: \sqrt{2}$

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(D) The kinetic energy of rotation $K$ is related to angular momentum $L$ and moment of inertia $I$ by the formula $K = \frac{L^2}{2I}$.Rearranging for angular momentum,we get $L = \sqrt{2KI}$.Since the kinetic energies $K$ are equal for both bodies,we have $L \propto \sqrt{I}$.Therefore,the ratio of the angular momenta of the two bodies is $\frac{L_1}{L_2} = \sqrt{\frac{I_1}{I_2}}$.Given $I_1 = I$ and $I_2 = 2I$,we substitute these values:$\frac{L_1}{L_2} = \sqrt{\frac{I}{2I}} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}$.Thus,the ratio is $1: \sqrt{2}$.

Two bodies have their moments of inertia $I$ and $2I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal,their angular momenta will be in the ratio

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