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Gravitation question

2005 · Q152
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Gravitation question

2005 · Q152

NEETPhysicsGravitationMCQ+4 / −1
For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is
  1. A
    1/2
  2. B
    1/2\sqrt 22​
  3. C
    2
  4. D
    2\sqrt 22​
View written solutionFree

Correct answer: A

K.E. of satellite moving in an orbit around the earth is

K=12mv2=12m(GMr)2=GMm2rK = {1 \over 2}m{v^2} = {1 \over 2}m{\left( {\sqrt {{{GM} \over r}} } \right)^2} = {{GMm} \over {2r}}K=21​mv2=21​m(rGM​​)2=2rGMm​

P.E. of satellite and earth system is

U=GMmrU = {{GMm} \over r}U=rGMm​

⇒KU=GMm2rGMmr=12 \Rightarrow {K \over U} = {{{{GMm} \over {2r}}} \over {{{GMm} \over r}}} = {1 \over 2}⇒UK​=rGMm​2rGMm​​=21​

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