Question

Two bodies of masses m and M are placed a distance d apart. The gravitational potential at the position were the gravitational field due to them is zero is

• A. $V=\frac{G}{d}(m+M)$
• B. $V=\frac{Gm}{d}$
• C. $V=\frac{GM}{d}$
• D. $V=\frac{G}{d}(\sqrt{m}+\sqrt{M})^2$

Answer 1

Answer: (D)

If net gravitational field of p becomes zero means
$\frac{Gm}{x^2} = \frac{GM}{(d - x)^2} \Rightarrow \, x = \frac{(\sqrt{m})d}{\sqrt{m} + \sqrt{M}}$ and $d - x = \frac{(\sqrt{M})d}{\sqrt{m} + \sqrt{M}}$
Gravitational potential at
$\frac{-Gm}{\frac{(\sqrt{m})d}{\sqrt{m} + \sqrt{M}}} + \frac{-Gm}{\frac{( \sqrt{M} )d}{\sqrt{m} + \sqrt{M}}} = - \frac{G}{d} (\sqrt{m} + \sqrt{M})^2$