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Question

# A satellite is revolving around earth with orbital speed v0. If it stops suddenly, find the speed with which it will strike the surface of earth. (ve= escape velocity).

A
v2ev0
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B
v0
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C
v2ev20
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D
v2e2v20
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Solution

## The correct option is D √v2e−2v20As the satellite is stopped suddenly we have is velocity as zero.Thus we get the initial energy of the satellite asE1=−GMmRNow when the satellite was in its circular orbit, the centripetal force is given asmv2oR=GMmR2ormv2o=GMmRorE1=−GMmR=−mv2oNow at the earth's surface, the total energy is given asE2=12mv2−GMReEquating the two energies we get−mv2o=12mv2−GMReorv2=−2v2o+2GMReorv2=v2e−2v2oorv=√v2e−2v2o

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