Question

A particle of mass $10$ g 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 them

• A. $13.34\times {10}^{-10}J$
• B. $3.33\times {10}^{-10}J$
• C. $6.67\times {10}^{-11}J$
• D. $6.67\times {10}^{-10}J$

Answer 1

Answer: (D)

$6.67\times {10}^{-10}J$

To take the particle far away from the sphere implies the gravitational potential is zero at that point, i.e. distance is infinite.
So, the work done is change in gravitational potential.
$W=\delta U=0-(-\frac{GMm}{r})=\frac{GMm}{r}$
$W=\frac{6.67\times {10}^{-11}\times 100\times 0.01}{0.1}=6.67\times {10}^{-10}J$
Option D.