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

Options

A. `13.34 xx 10^-10 J`
B. `3.33 xx 10^-10 J`
C. `6.67 xx 10^-9 J`
D. `6.67 xx 10^-10 J`

Answer

D

Explanation

`U_i = - (GMm)/( r)`
`U_i = - (6.67 xx 10^-11 xx 100 xx 10^-2)/(0.1)`
`U_i = -(6.67 xx 10^-11)/(0.1)`
=`-6.67 xx 10^-10 J`
We know that
`W = Delta U`
=`U_f - U_i" "(because U_f = 0)`
`:. W = U_i = 6.67 xx 10^-10 J`.