Two rigid bodies A and B rotate with rotation | vedclass

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(C) The rotational kinetic energy $E$ of a body is related to its angular momentum $L$ and moment of inertia $I$ by the formula $E = \frac{L^2}{2I}$.R

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(C) The rotational kinetic energy $E$ of a body is related to its angular momentum $L$ and moment of inertia $I$ by the formula $E = \frac{L^2}{2I}$.Rearranging this formula to solve for angular momentum,we get $L = \sqrt{2EI}$.Now,we find the ratio of the angular momentum of $A$ to that of $B$:$\frac{L_A}{L_B} = \frac{\sqrt{2E_A I_A}}{\sqrt{2E_B I_B}} = \sqrt{\frac{E_A}{E_B} 	imes \frac{I_A}{I_B}}$.Given that $E_A = 100E_B$ and $I_A = \frac{I_B}{4}$,we substitute these values into the ratio:$\frac{L_A}{L_B} = \sqrt{100 	imes \frac{1}{4}} = \sqrt{25} = 5$.Thus,the ratio of the angular momentum of $A$ to $B$ is $5$.

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