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 done against the gravitational force between them to take the particle far away from the sphere.

• A. $13.34\times {10}^{-10}$J
• B. $3.33\times {10}^{-10}$J
• C. $6.67\times {10}^{-9}$J
• D. $6.67\times {10}^{-10}$J

Answer 1

The correct option is D $6.67\times {10}^{-10}$J

$△W=Workdone=FinalPotentialEnergy-InitialPotentialEnergy$

Now, final potential energy$=0$ because ATQ, the particle of mass is taken far away.

$\Rightarrow R\to \infty$

$\Rightarrow v_1=0$

For Initial potential energy$=\frac{-GMm}{R}$

$=\frac{-6.67\times {10}^{-11}\times 100\times 10}{0.1\times 1000}=-6.67\times {10}^{-10}J$

Substituting the values we get,

$△W=0-(-6.67\times {10}^{-10})J=6.67\times {10}^{-10}J$