Two bodies have their moments of inertia I an | vedclass

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(C) The rotational kinetic energy $K$ is given by $K = \frac{L^2}{2I}$,where $L$ is the angular momentum and $I$ is the moment of inertia.Given that t

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$1: \sqrt{2}$

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(C) The rotational kinetic energy $K$ is given by $K = \frac{L^2}{2I}$,where $L$ is the angular momentum and $I$ is the moment of inertia.Given that the kinetic energies are equal,$K_1 = K_2$.Therefore,$\frac{L_1^2}{2I_1} = \frac{L_2^2}{2I_2}$.Substituting $I_1 = I$ and $I_2 = 2I$:$\frac{L_1^2}{2I} = \frac{L_2^2}{2(2I)}$$\frac{L_1^2}{I} = \frac{L_2^2}{2I}$$\frac{L_1^2}{L_2^2} = \frac{I}{2I} = \frac{1}{2}$Taking the square root on both sides:$\frac{L_1}{L_2} = \frac{1}{\sqrt{2}}$Thus,the ratio of their angular momenta is $1: \sqrt{2}$.

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

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