Question

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

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

Answer 1

The correct option is D $V=-\frac{G}{d}{(\sqrt{m}+\sqrt{M})}^2$

Let that point be $x$ distance from $m$

Then $\frac{-GM}{(d-x{)}^2}=\frac{-Gm}{x^2}$

$\Rightarrow \frac{d-x}{x}=\sqrt{\frac{M}{m}}$

$Potential=-\frac{GM}{d-x}-\frac{Gm}{x}$

$Potential=\frac{-G}{d}(\sqrt{M}+\sqrt{m}{)}^2$