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 $\frac{\omega _{1}}{\omega _{2}}=\sqrt{\frac{I_{2}}{I_{1}}}$ .
$\frac{L_{1}}{L_{2}}=\frac{I_{1} \omega _{1}}{I_{2} \omega _{2}}=\frac{I_{1}}{I_{2}}\sqrt{\frac{I_{2}}{I_{1}}}=\sqrt{\frac{I_{1}}{I_{2}}}$
$\frac{L_{1}}{L_{2}}=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}}$ .