Two bodies have their moments of inertia I and 2I respectively about their axes of rotation. If their…
Two bodies have their moments of inertia I and 2I respectively about their axes of
rotation. If their kinetic energies of rotation are equal, their angular momenta will
be in the ratio
$2: 1$
$1: 2 \sqrt{2}$
$1: \sqrt{2}$
$1: 2$
Solution
$\begin{array}{l}
(\mathrm{kE})_{1}=(\mathrm{kE})_{2} \\
\therefore \frac{1}{2} \mathrm{I} \omega_{1}^{2}=\frac{1}{2}(2 \mathrm{I}) \omega_{2}^{2} \\
\therefore \frac{\omega_{1}^{2}}{\omega_{2}^{2}}=2 \\
\therefore \frac{\omega_{1}}{\omega_{2}}=\sqrt{2}
\end{array}$
Ratio of angular momenta $=\frac{I \omega_{1}}{2 I \omega_{2}}=\frac{1}{2} \frac{\omega_{1}}{\omega_{2}}=\frac{1}{\sqrt{2}}$