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 momenta will be in the ratio-

• A. $\sqrt{\frac{3}{1}}$
• B. $\sqrt{\frac{6}{1}}$
• C. $\sqrt{\frac{2}{1}}$
• D. $\sqrt{\frac{5}{1}}$

Answer 1

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

$\frac{1}{2}\ast i_1\ast {\omega }_1^2=\frac{1}{2}\ast i_2\ast {\omega }_2^2$

here $i_1=l,i_2=2l$

$\frac{{\omega }_1}{{\omega }_2}=\sqrt{\frac{2}{1}}$