AIIMS 2019 Physics Gravitational Potential Energy MCQ Question

To find the work done against the gravitational force to move the particle far away from the sphere, we use the formula for gravitational potential energy: $U = -\frac{G m_1 m_2}{r}$, where $m_1$ is the mass of the sphere (100 kg), $m_2$ is the mass of the particle (0.01 kg), $r$ is the distance from the center of the sphere (0.1 m), and $G$ is the gravitational constant $6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$. Calculating this gives $U = -6.67 \times 10^{-9} \, \text{J}$, and the work done to move the particle to infinity is the positive of this potential energy, resulting in $6.67 \times 10^{-9} \, \text{J}$ (option D).

Options A, B, and C are incorrect because they do not accurately reflect the calculated gravitational potential energy or the work required to overcome it, either underestimating or miscalculating the values involved.