A particle of mass 10g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them, to take the particle far away from the sphere (you may take `G=6.67xx10^(-11)Nm^(2)//kg^(2))`

Options

A. `6.67xx10^(-9)J`
B. `6.67xx10^(-10)J`
C. `3.33xx10^(-10)J`
D. `13.34xx10^(-10)J`

Answer

B

Explanation

Initial distance of the body from the centre of the sphere `=10 cm =0.1 m = d_(1)=10^(-1)m`
and final distance of the body `= oo = d_(2)`
`therefore` The work done in taking a body far away from the sphere against the gravitational force between them
= Change in gravitational potential energy
i.e. `U_(2)-U_(1)`
`= -(GMm)/(d_(2))-(-(GMm)/(d_(1)))`
`=-(GMm)/(oo)+(GMm)/(0.1)=0+(GMm)/(0.1)`
`therefore U_(2)-U_(1)=(GMm)/(0.1)`
`=(6.67xx10^(-11)xx100xx10xx10^(-3))/(10^(-1))`
`=6.67xx10^(-10)J`