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Question

# A satellite is revolving around earth in a circular orbit of radius 2R, where R is the earth's radius. A particle is projected from this satellite radially outward relative to satellite with speed u. Find the minimum value of u so that particle escapes the gravitational force of earth. M is the mass of earth. (Mass of earth >>> Mass of satellite >>> Mass of particle)

A
GMR
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B
GM2R
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C
2GMR
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D
2GMR
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Solution

## The correct option is B √GM2RThe particle already has one component of velocity i.e. √GM2R. If it projected with velocity of u radially outwards, let u1 be its magnitude of velocity. So, u2+GM2R=u21 ⇒u1=√u2+GM2R.....(1) Using energy conservation, we can say: 12mu21−GMm2R=0⇒u1=√GMRFrom( 1) ⇒GM2R+u2=GMR u=√GM2R

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