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Question

# A body is released from a height equal to radius(R) of the earth. The velocity of body when it strikes the surface of the earth will be :

A
gR
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B
2gR
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C
gR
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D
2gR
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Solution

## The correct option is C gRThe potential energy of a mass m at a distance r from the center of the earth (assumed to be a spherically symmetric object of mass M and radius R) isVr=GMmrInitially the mass is at rest at r=2Rits total energy isV(2R)=GMm2RThus, from the law of conversation of energy its speed v when it hits the earth (at r=R) is given by12mv2GMmR=GMm2R12mv2=GMm(R1R2)=GMmR2V2=GMRNow, the force on the mass at the surface of the earth is given bymg=GMmR2g=GMR2 ThusV2=gRv=gR

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