Question

Two bodies have their moments of inertia I and $2$I 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. $\sqrt{2}:1$
• C. $1:\sqrt{2}$
• D. $2:1$

Answer 1

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

$KE=\frac{1}{2}{I\omega }^2=\frac{1}{2}\frac{L^2}{I}$

${KE}_1={KE}_2$

$\frac{1}{2}\frac{L_1^2}{I_1}=\frac{1}{2}\frac{L_2^2}{I_2}$

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

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

$1:\sqrt{2}$