Q 11-07-008NEETNEET 2023Top questionMedium
Two bodies of mass $m$ and $9m$ are placed at a distance $R$. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be ($G$ = gravitational constant) :
Answer: (C) $-\dfrac{16Gm}{R}$
Let the null point be at distance $x$ from $m$:
$$\frac{Gm}{x^2} = \frac{G(9m)}{(R - x)^2} \;\Rightarrow\; \frac{R - x}{x} = 3 \;\Rightarrow\; x = \frac{R}{4}$$
Potential there:
$$V = -\frac{Gm}{R/4} - \frac{9Gm}{3R/4} = -\frac{4Gm}{R} - \frac{12Gm}{R} = -\frac{16Gm}{R}$$
Solution by Sreeraj P, M.Sc Physics