Two bodies of masses m and M are placed a distance d apart. The gravitational potential at the position where the gravitational field due to them is zero is V, then :
Answer & explanation
Correct answer: option 1
If P is the point of zero intensity, then :
\(x = \frac{\sqrt{M}}{\sqrt{M} + \sqrt{m}}.d \text{ and }\)
\(d - x = d - \frac{\sqrt{M}}{\sqrt{M} + \sqrt{m}}.d \text{ and }\)
Now potential at point P,
\(V = V_1 + V_2\)
\(V = -\frac{GM}{x} - \frac{GM}{d-x}\)
\(V = - \frac{G}{d} (\sqrt{m} + \sqrt{M})^2\)