Q112 / 200 · NEET 2005 · Physics

Two bodies have their moments of inertia $l$ and $2 l$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio:

  • A
    $2: 1$
  • B
    $1: 2$
  • C
    $\sqrt{2}: 1$
  • Correct answer
    D
    $1: \sqrt{2}$

Solution

K.E. rotation $K=\frac{1}{2} I \omega^2$ Angular momenta $L=100$ $\therefore \quad K=\frac{L^2}{2}$ Here $K_1+K_2, I_1=I_1, I_2=21$ $$ \therefore \quad \frac{L_1}{L_2}=\sqrt{\frac{2 I_1 K_1}{2 I_2 K_2}} $$ $$ \begin{aligned} & =\sqrt{\frac{I_1}{I_2}}=\sqrt{\frac{I}{2 I}} \\ & =\frac{1}{\sqrt{2}} \end{aligned} $$

Hence, the correct answer is option: 'D'.

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