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 momentum will be in the ratio

Q: 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 momentum will be in the ratio

(a) 1 : 2

(b) √2 : 1

(c) 2 : 1

(d) 1 : √2

Ans: (d)

Sol: $\frac{L_1^2}{2 I_1} = \frac{L_2^2}{2 I_2} $

$\frac{L_1^2}{L_2^2} = \frac{I_1}{I_2} $

$\frac{L_1^2}{L_2^2} = \frac{I}{2 I} $

$\frac{L_1}{L_2} = \frac{1}{\sqrt{2} } $