Gravitational Potential: Practice Problem & Solution

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Gravitational Potential. Understanding the underlying formula is key to arriving at the correct answer below:

Let the point of zero field be at distance \(r_1\) from \(m\) and \(r_2\) from \(M\). Then \(\frac{\sqrt{m}}{r_1} = \frac{\sqrt{M}}{r_2}\), with \(r_1 + r_2 = d\). Solving gives \(r_1 = \frac{\sqrt{m}d}{\sqrt{m}+\sqrt{M}}\) and \(r_2 = \frac{\sqrt{M}d}{\sqrt{m}+\sqrt{M}}\). Thus, \(V = -\frac{Gm}{r_1} - \frac{GM}{r_2} = -\frac{G}{d}(\sqrt{m}+\sqrt{M})^2\).