Two rotating bodies $A$ and $B$ of masses $m$ and $2 m$ with moments of inertia $I_{A}$ and $I_{B}\l

Question

Two rotating bodies $A$ and $B$ of masses $m$ and $2 m$ with moments of inertia $I_{A}$ and $I_{B}\left(I_{B}>I_{A}ight)$ have equal kinetic energy of rotation. If $L_{A}$ and $L_{B}$ be their angular momenta respectively, then\

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(c): Here, $m_{A}=m, m_{B}=2 m$ Both bodies $A$ and $B$ have equal kinetic energy of rotation $$ K_{A}=K_{B} \Rightarrow \frac{1}{2} I_{A} \omega_{A}^{2}=\frac{1}{2} I_{B} \omega_{B}^{2} 	ag{i} $$ $\Rightarrow \frac{\omega_{A}^{2}}{\omega_{B^{\prime}}^{2}}=\frac{I_{B}}{I_{A}}$\ Ratio of angular momenta, $$ \begin{array}{rlr} \frac{L_{A}}{L_{B}} & =\frac{I_{A} \omega_{A}}{I_{B} \omega_{B}}=\frac{I_{A}}{I_{B}} 	imes \sqrt{\frac{I_{B}}{I_{A}}} & 	ext { [Using eqn. (i)] } \ & =\sqrt{\frac{I_{A}}{I_{B}}}<1 & \left(\because I_{B}>I_{A}ight) \end{array} $$ $	herefore \quad L_{B}>L_{A}$\