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# For two satellites at distances R and 7R above the earth's surface, the ratio of their

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a
total energies is 4 and potential and kinetic energies is 2
b
potential energies is 4
c
kinetic energies is 4
d
total energies is 4

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detailed solution

Correct option is B

Distances of the two satellites from the centre of the earth are r1 = 2R and r2 = 8R, respectively (R = earth's radius. Their potential energies are            V1=−GmMr1 and V2=−GmMr2Their ratio is V1V2=r2r1=8R2R=4The kinetic energy of a satellite can be obtained from the relation          mv2r=GmMr2or      K=12mv2=GmM2r          K1=GmM2r1 and K2=GmM2r2The ratio of their kinetic energies is       K1K2=r2r1=8R2R=4Their total energies are E1=−GmMr1+GmM2r1=−GmM2r1and   E2=−GmMr2+GmM2r2=−GmM2r2Their ratio is E1E2=r2r1=8R2R=4Hence, the correct choices are (2), (3) and (4).

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