Q128 / 155 · WBJEE 2024 · Physics
A satellite of mass m rotates round the earth in a circular orbit of radius R. If the angular momentum of the satellite
is J, then its kinetic energy (K) and the total energy (E) of the satellite are
- A$\mathrm{K}=\frac{\mathrm{J}^2}{m R^2}, \mathrm{E}=-\frac{\mathrm{J}^2}{2 m R^2}$
- Correct answerB$\mathrm{K}=\frac{\mathrm{J}^2}{2 m R^2}, \mathrm{E}=-\frac{\mathrm{J}^2}{2 m R^2}$
- C$\mathrm{K}=\frac{J^2}{2 m R^2}, \mathrm{E}=-\frac{J^2}{m R^2}$
- D$K=\frac{J^2}{2 m R^2}, E=\frac{J^2}{m R^2}$
Solution
where "I, is moment of inertia"
Hint: $K E=\frac{J^2}{2 I}=\frac{J^2}{2 m R^2}, \quad E=-K E$
Hence, the correct answer is option: 'B'.