Gravitational Potential: Practice Problem & Solution
Two bodies of masses \(m\) and \(M\) are placed at distance \(d\) apart. What is the gravitational potential \(V\) at the position where the gravitational field due to them is zero?
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:
At the point where the field is zero, \(\frac{Gm}{r_1^2} = \frac{GM}{r_2^2}\), which gives \(r_1 = \frac{\sqrt{m}}{\sqrt{m} + \sqrt{M}} d\) and \(r_2 = \frac{\sqrt{M}}{\sqrt{m} + \sqrt{M}} d\). The potential is \(V = -\frac{Gm}{r_1} - \frac{GM}{r_2} = -\frac{G}{d}(\sqrt{m} + \sqrt{M})^2\).
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