Q108 / 180 · AIIMS 2018 (26 May) · Physics

A satellite is revolving around the earth with a kinetic energy $E$. The minimum addition of kinetic energy needed to make it escape from its orbit is

  • A
    $2 E$
  • B
    $\sqrt{E}$
  • C
    $E / 2$
  • Correct answer
    D
    $E$

Solution

(d): Orbital velocity of satellite, $v_0=\sqrt{\frac{G M}{r}}$ Kinetic energy, $E=\frac{1}{2} m v_0^2=\frac{1}{2} \frac{G M m}{r}$ Kinetic energy for escaping, $\begin{aligned} E^{\prime}=\frac{1}{2} m v_e^2 & =\frac{1}{2} m \frac{2 G M}{r}=\frac{G M m}{r} \\ & =2 E \quad\left(\because v_e=\sqrt{\frac{2 G M}{r}}\right)\end{aligned}$ Additional kinetic energy needed $=E^{\prime}-E=2 E-E=E$

Hence, the correct answer is option: 'D'.

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