Question

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

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

Answer 1

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



We know that,

$W=\Delta U$

$=U_f-U_i(\because U_f=0)$

$W=-U_0$

$=\frac{GMm}{R}\{\because U_i=-\frac{GMm}{R}\}$

$W=\frac{6.67\times {10}^{-11}\times 100\times 10\times {10}^{-3}}{0.1}$

$W=6.67\times {10}^{-10}\text{J}$