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 answer
    B
    $\mathrm{K}=\frac{\mathrm{J}^2}{2 m R^2}, \mathrm{E}=-\frac{\mathrm{J}^2}{2 m R^2}$
  • 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'.

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