Question

If two bodies have moments of inertia $I$ and $2I$ respectively about their axis of rotation and their kinetic energies of rotation are also known to be equal, then find the ratio of their angular momenta.

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

Answer 1

Answer: (C)

As $k_{R_1}=k_{R_2}$ .
$\therefore \frac{1}{2}{I}_1{\omega }_1^2=\frac{1}{2}{I}_2{\omega }_2^2$
Or $\frac{{\omega }_1}{{\omega }_2}=\sqrt{\frac{I_2}{I_1}}$ .
$\frac{L_1}{L_2}=\frac{I_1{\omega }_1}{I_2{\omega }_2}=\frac{I_1}{I_2}\sqrt{\frac{I_2}{I_1}}=\sqrt{\frac{I_1}{I_2}}$
$\frac{L_1}{L_2}=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}}$ .