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AIIMS 2016
Exam
AIIMS
Year
2016
Subject
Physics
Chapter
Gravitation

AIIMS 2016 · Physics · Gravitation

The additional kinetic energy to be provided to a satellite of mass...

The additional kinetic energy to be provided to a satellite of mass mm revolving around a planet of mass MM to transfer it from a circular orbit of radius R1R_1 to another of radius R2(R2>R1)R_2\left(R_2>R_1\right) is

Options

  1. AGmM(1R12−1R22)G m M\left(\frac{1}{R_1^2}-\frac{1}{R_2^2}\right)
  2. BGmM(1R1−1R2)G m M\left(\frac{1}{R_1}-\frac{1}{R_2}\right)
  3. C2GmM(1R1−1R2)2 G m M\left(\frac{1}{R_1}-\frac{1}{R_2}\right)
  4. D12GmM(1R1−1R2)\frac{1}{2} G m M\left(\frac{1}{R_1}-\frac{1}{R_2}\right)

Correct answer

D. 12GmM(1R1−1R2)\frac{1}{2} G m M\left(\frac{1}{R_1}-\frac{1}{R_2}\right)

Step-by-step solution

As−GMm2R1+KE=−GMm2R2KE=12GMm(1R1−1R2).\begin{aligned} & \mathrm{As}-\frac{G M m}{2 R_1}+\mathrm{KE}=\frac{-G M m}{2 R_2} \\ & \mathrm{KE}=\frac{1}{2} G M m\left(\frac{1}{R_1}-\frac{1}{R_2}\right) .\end{aligned}
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