Q. 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) $6.67 \times 10^{- 10}J$
Explanation
(d) $\ \ \ \ \ \ \ \ \ \ \ U_{i} = - \frac{GMm}{r}$
$\ \ \ \ \ \ \ \ \ \ U_{i} = \frac{6.67 \times 10^{- 11} \times 100 \times 10^{- 2}}{0.1}$
$\ \ \ \ \ \ \ \ \ U_{i} = - \frac{6.67 \times 10^{- 11}}{0.1}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = - 6.67 \times 10^{- 10}J$
We know
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ W = \mathrm{\Delta}U$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = U_{f} - U_{i\ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left( \therefore U_{f} = 0 \right)$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ W = U_{i} = 6.67 \times 10^{- 10}J$
[image:8_image69.emf]
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.