System Of Particles And Rotational Motion Ques 40

40. 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 momenta will be in the ratio

[2005]

(a) $2: 1$

(b) $1: 2$

(c) $\sqrt{2}: 1$

(d) $1: \sqrt{2}$

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Answer:

Correct Answer: 40.(d)

Solution:

  1. (d) The relation between K.E. of rotation and angular momentum,

$ \begin{aligned} & K=\frac{L^{2}}{2 I} \Rightarrow L^{2}=2 K I \Rightarrow L=\sqrt{2 K I} \\ & \frac{L_1}{L_2}=\sqrt{(\frac{K_1}{K_2})(\frac{I_1}{I_2})}=\sqrt{(\frac{K}{K})(\frac{I}{2 I})}=\frac{1}{\sqrt{2}} \\ & L_1: L_2=1: \sqrt{2} \end{aligned} $

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