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NEET 2016
Exam
NEET
Year
2016
Subject
Physics
Chapter
Gravitation

NEET 2016 · Physics · Gravitation

A satellite of mass m is orbiting the earth (of radius R ) at a...

A satellite of mass mm is orbiting the earth (of radius RR) at a height hh from its surface. The total energy of the satellite in terms of go{g}_{o} , the value of acceleration due to gravity at the earth's surface, is

Options

  1. A\dfrac{m{g}_{0}{R}^{2}}{2\left(R + h\right)}
  2. B- \dfrac{m{g}_{0}{R}^{2}}{2\left(R + h\right)}
  3. C2mg0R2R+h\dfrac{2m{g}_{0}{R}^{2}}{R + h}
  4. D−2mg0R2R+h- \dfrac{2m{g}_{0}{R}^{2}}{R + h}

Correct answer

B. - \dfrac{m{g}_{0}{R}^{2}}{2\left(R + h\right)}

Step-by-step solution

The total energy of a satellite in the orbit is

E=−GMm2rE = - \dfrac{GMm}{2r}

r=R+hr = R + h

g0=GMR2{g}_{0} = \dfrac{GM}{{R}^{2}}
⇒E=−mg0R22(R+h)⇒ E = - \dfrac{m{g}_{0}{R}^{2}}{2\left(R + h\right)}

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