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AIIMS 201826 May
Exam
AIIMS
Year
2018
Date
26 May
Subject
Physics
Chapter
Gravitation

AIIMS 2018 · 26 May · Physics · Gravitation

A satellite is revolving around the earth with a kinetic energy E ....

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

Options

  1. A2E2 E
  2. BE\sqrt{E}
  3. CE/2E / 2
  4. DEE

Correct answer

D. EE

Step-by-step solution

(d): Orbital velocity of satellite, v0=GMrv_0=\sqrt{\frac{G M}{r}} Kinetic energy, E=12mv02=12GMmrE=\frac{1}{2} m v_0^2=\frac{1}{2} \frac{G M m}{r} Kinetic energy for escaping, E′=12mve2=12m2GMr=GMmr=2E(∵ve=2GMr)\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
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