Two rigid bodies A and B rotate with rotational kinetic energies E_A and E_B respectively. mom

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6.System of Particles and Rotational Motion

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Two rigid bodies $A$ and $B$ rotate with rotational kinetic energies $E_A$ and $E_B$ respectively. The moments of inertia of $A$ and $B$ about the axis of rotation are $I_A$ and $I_B$ respectively. If $I_A = I_B/4 \,$and$ \, E_A = 100\ E_B$ the ratio of angular momentum $(L_A)$ of $A$ to the angular momentum $(L_B)$ of $B$ is

A

$25$

B

$5/4$

C

$5$

D

$1/4$

Solution

$E_{\text {retational}}=\frac{1}{2} I w^{2}=\frac{L^{2}}{2 I} \quad(\text {where}, L=\quad I w)$

Therefore, $L^{2}=2 E I$

Hence, $\Rightarrow L_{A}^{2}=2 E_{A} I_{A}…….(1)$

$\Rightarrow L_{B}^{2}=2 E_{B} I_{B}…….(2)$

From equation $( 1 )$ and $( 2 )$

$\Rightarrow \frac{L_{A}}{L_{B}}=5$

Standard 11

Physics

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