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Gravitation question

2010 · Q176
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Gravitation question

2010 · Q176

NEETPhysicsGravitationMCQ+4 / −1
The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If the speed of satellite A is 3V, then the speed of satellite B will be
  1. A
    3V4{{3V} \over 4}43V​
  2. B
    6VVV
  3. C
    12VVV
  4. D
    3V2{{3V} \over 2}23V​
View written solutionFree

Correct answer: B

Orbital velocity of a satellite in a circular orbit of radius a is given by

v=GMav = \sqrt {{{GM} \over a}} v=aGM​​

⇒v∝1a\Rightarrow v \propto \sqrt {{1 \over a}}⇒v∝a1​​

⇒v2v1=a1a2\Rightarrow {{{v_2}} \over {{v_1}}} = \sqrt {{{{a_1}} \over {{a_2}}}}⇒v1​v2​​=a2​a1​​​

∴\therefore∴ v2=v14RR{v_2} = {v_1}\sqrt {{{4R} \over R}} v2​=v1​R4R​​ = 2v1 = 6V

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