Question

# A particle of mass 10gm is kept on the surface of a uniform sphere of mass 100kg and radius 10cm. Find the work done against the gravitational force between them, to take the particle far away from the sphere. (G=6.67×10−11Nm2/Kg2)

A
3.33×109J
B
3.33×1010J
C
6.67×109J
D
6.67×1010J
Solution
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#### At infinity, the gravitational potential energy of the system will be 0.Initially, the particle is outside sphere and hence sphere will behave as point object at its centre,Therefore,E0=−GMmR=−(6.67×10−11)×(100)×(0.01)0.1=−6.67×10−10JWe know that, W=ΔU=Uf−Ui⟹W=−UiThus, work done is 6.67×10−10J

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