Question

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:

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

Answer 1

The correct option is D $1:\sqrt{2}$

Relation between angular momentum and kinetic energy is $L=\sqrt{2I{E}_k}$
Here, kinetic energy $\left(E_k\right)$ is constant, $\therefore L\propto \sqrt{I}$
$\frac{L_1}{L_2}=\sqrt{\frac{I}{2I}}=\frac{1}{\sqrt{2}}$