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The work done liftting a particle of mas...

The work done liftting a particle of mass 'm' from the centre of the earth to the surface of the earth is

A

`-mgR`

B

` + (mgR)/(2)`

C

0

D

`- (mg R)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Gravitational potential energy at the centre of earth is
` U_i = - (3GmM)/(2R) = -3/2 gRm " " ( because g = (GM)/(R^2) )`
Gravitational potential energy at the surface of earth is
`U_f = -(GMm)/( R) = - mgR`
Work done , ` W = U_f - U_i =-mgR - (-3/2 mg R) = (mg R)/(2)`
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