Two bodies of moment of inertia $I_{1}$ and $I_{2}$ $(I_{1} I_{2})$ have equal angular momenta. If $E_{1},E_{2}$ are their kinetic energies of rotation, then

Question

Two bodies of moment of inertia $I_{1}$ and $I_{2}$ $(I_{1} > I_{2})$ have equal angular momenta. If $E_{1},E_{2}$ are their kinetic energies of rotation, then

Dr. Abubacker · Accepted Answer

(c) $I_{1}\omega_{1} = I_{2}\omega_{2}\ \ \ 	herefore\frac{\omega_{1}}{\omega_{2}} = \frac{I_{2}}{I_{1}}$
Now, $\frac{E_{1}}{E_{2}} = \frac{\frac{1}{2}I_{1}\omega_{1}^{2}}{\frac{1}{2}I_{2}\omega_{2}^{2}} = \frac{I_{1}}{I_{2}} 	imes \left( \frac{I_{2}}{I_{1}} ight)^{2} = \frac{I_{2}}{I_{1}}$
As $I_{1} > I_{2}\ 	herefore E_{1} < E_{2}$

Q. Two bodies of moment of inertia $I_{1}$ and $I_{2}$ $(I_{1} > I_{2})$ have equal angular momenta. If $E_{1},E_{2}$ are their kinetic energies of rotation, then

Explanation

Reviewed by Dr. Abubacker

Want more practice?