Two bodies have their moments of inertia I an | vedclass

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(D) The rotational kinetic energy $(KE)$ is related to the angular momentum $(L)$ and moment of inertia $(I)$ by the formula: $KE = \frac{L^2}{2I}$.Gi

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$1:\sqrt{2}$

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(D) The rotational kinetic energy $(KE)$ is related to the angular momentum $(L)$ and moment of inertia $(I)$ by the formula: $KE = \frac{L^2}{2I}$.Given that the rotational kinetic energies are equal $(KE_1 = KE_2)$,we have:$\frac{L_1^2}{2I_1} = \frac{L_2^2}{2I_2}$Substituting the given values $I_1 = I$ 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 axis of rotation. If their kinetic energies of rotation are equal,their angular momentum will be in the ratio

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