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 the sphere (you may take $G=6.67 \times 10^{-11} Nm ^{2} / kg ^{2}$ )

• 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

$ U_{i} =-\frac{G M m}{r}$ $ U_{i} =-\frac{6.67 \times 10^{-11} \times 100 \times 10^{-2}}{0.1} $

$U_{i} =-\frac{6.67 \times 10^{-11}}{0.1}$ $=-6.67 \times 10^{-10} J$ We know $\therefore W =\Delta U $ $=U_{f}-U_{l} \left(\because U_{f}=0\right) $ $W =-U_{i}=6.67 \times 10^{-10} J$