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Q.

A satellite of mass  m is orbiting the earth (of radius R ) at a height h from its surface. The potential energy and kinetic total energy of the satellite will be respectively:

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a

-mg0R22(R+h), mg0R22(R+h)

b

-mg0R2(R+h)mg0R22(R+h)

c

-2mg0R2R+h, mg0R22(R+h)

d

-2mg0R2R+h, 2mg0R2R+h

answer is B.

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Detailed Solution

Potential energy of satellite at height  h  from the earth surface, 

P.E. = -GMm(R+h)=-mg0R2(R+h)g0=GMR2

Kinetic energy (K.E.) =  12mv2

 Also, mv2(R+h)=GMm(R+h)2 or, v2=GMR+h…..(2)

K.E. = GMm2R+h=mg0R22(R+h)g0=GMR2

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