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Gravitation question

2012 · Q100
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Gravitation question

2012 · Q100

NEETPhysicsGravitationMCQ+4 / −1
If ve{v_e}ve​ is escape velocity and vo{v_o}vo​ is orbital velocity of a satellite for orbit close to the earth's surface, then these are related by
  1. A
    vo=2ve{v_o} = \sqrt {2{v_e}}vo​=2ve​​
  2. B
    vo === ve
  3. C
    ve=2vo{v_e} = \sqrt {2{v_o}}ve​=2vo​​
  4. D
    ve=2vo{v_e} = \sqrt 2 {v_o}ve​=2​vo​
View written solutionFree

Correct answer: D

Escapevelocity, ve=2GMR{v_e} = \sqrt {{{2GM} \over R}} ve​=R2GM​​    ...(i)

where M and R where M and R be the mass and radius of the earth respectively. The orbital velocity of a satellite close to the earth’s surface is

v0=GMR{v_0} = \sqrt {{{GM} \over R}} v0​=RGM​​   ...(ii)

From (i) and (ii), we get

ve=2v0{v_e} = \sqrt 2 {v_0}ve​=2​v0​

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