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Question

A satellite is orbiting around the earth in a circular orbit of radius r. A particle of mass m is projected from the satellite in a forward direction with a velocity v=2/3 times the orbital velocity (this velocity is given w.r.t earth). During subsequent motion of the particle, its minimum distance from the centre of earth is

A
2r7
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B
r
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C
2r3
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D
4r5
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Solution

The correct option is A 2r7
Since in this case, the particle will move in elleptical orbit, the minimum distance will be at a position opposite to the initial position.

Conserving angular momentum,

mr(23GMr)=mvx

Also, conserving total energy,

12m(49GMr)GMmr=12mv2GMmx

GMx12v2=79GMr

GMx12(vx)2=79GMrx2

GMx29GMr=79GMrx2

x=2r7

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