Q. Two rigid bodies $A$ and $B$ rotate with rotational kinetic energies $E_{A}$ and $E_{B}$ respectively. The moments of inertia of $A$ and $B$ about the axis of rotation are $I_{A}$ and $I_{B}$ respectively. If $I_{A} = I_{B}/4$ and $E_{A} = 100\ E_{B}$ the ratio of angular momentum $(L_{A})$ of $A$ to the angular momentum $(L_{B})$ of $B$ is
A) 25
B) 5/4
C) 5
D) 1/4
Explanation
(c) Rotational kinetic energy $E = \frac{L^{2}}{2I}\ \therefore L = \sqrt{2EI}$
$\Rightarrow \frac{L_{A}}{L_{B}} = \sqrt{\frac{E_{A}}{E_{B}} \times \frac{I_{A}}{I_{B}}} = \sqrt{100 \times \frac{1}{4}} = 5$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.