Potential at Zero Field Position – Rankers Physics
Topic: Gravitation
Subtopic: Gravitational Potential

Potential at Zero Field Position

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?
\(V = -\frac{G}{d}(m + M)\)
\(V = -\frac{G}{d} m\)
\(V = -\frac{GM}{d}\)
\(V = -\frac{G}{d}(\sqrt{m} + \sqrt{M})^2\)

Solution:

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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