A particle of mass `1 kg` is kept on the surface of a uniform sphere of mass `20 kg` and radius `1.0 m`. Find the work to be done against the gravitational force between them to take the particle away from the sphere.

Explanation

Potential at the surface of thin spherical shell,
`V=-(GM)/(R)=-((6.67xx10^(-11))(20))/(1)"J kg"^(-1)`
`=1.334 xx10^(-9)"J kg"^(-1)`
i.e., `1.334 xx 10^(-9)J` work is obtained to bring a mass of 1kg from infinity to the surface of shell. Hence, the same amount of work will have to be done to take the particle away from the surface of shell. Thus,
`W=1.334xx10^(-9)J`