Q100 / 180 · AIIMS 2018 (27 May) · Physics
A satellite is moving with a constant speed $v$ in a circular orbit about the earth. An object of mass $m$ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is
- A$\frac{1}{2} m v^2$
- Correct answerB$m v^2$
- C$\frac{1}{3} m v^2$
- D$\frac{2}{3} m v^2$
Solution
Escape speed,
$v_e=\sqrt{2} \times$ orbital speed $=\sqrt{2} v$
$\therefore \quad$ Kinetic energy of the object at the time of ejection $=\frac{1}{2} m v_e^2=\frac{1}{2} m(\sqrt{2} v)^2=m v^2$
Hence, the correct answer is option: 'B'.