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A satellite of mass m is orbiting around...

A satellite of mass m is orbiting around the earth at a height equal to twice the radius of the earth (R). Its potential energy is given by

A

`-2mgR`

B

`-mg.(R)/(2)`

C

`(-2)/(3)mgR`

D

`-mg.(R)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`PE = int_(R)^(3R) - (GMm)/(r^(2)) dr`
`=- GMm [(r^(-1))/(-1)]_(R)^(3R) = GMm [(1)/(3R)-(1)/(R)]`
`=- (2)/(3)(GMm)/(R) =- (2)/(3) (gR^(2)m)/(R) =- (2)/(3)mgR`
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