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. $(G=6.67\times {10}^{-11}N{m}^2/K{g}^2)$

• A. $3.33\times {10}^{-9}J$
• B. $3.33\times {10}^{-10}J$
• C. $6.67\times {10}^{-9}J$
• D. $6.67\times {10}^{-10}J$

Answer 1

Answer: (D)

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

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,

$E_0=-\frac{GMm}{R}=-\frac{(6.67\times {10}^{-11})\times \left(100\right)\times \left(0.01\right)}{0.1}=-6.67\times {10}^{-10}J$
We know that, $W=\Delta U=U_f-U_i⟹W=-U_i$

Thus, work done is $6.67\times {10}^{-10}J$