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(C) Let the gravitational field at point $P$,at a distance $x$ from mass $m$,be zero.Equating the gravitational field strengths due to both masses:$\f

Vedclass · Accepted Answer

$-\frac{9Gm}{r}$

Vedclass · Answer

(C) Let the gravitational field at point $P$,at a distance $x$ from mass $m$,be zero.Equating the gravitational field strengths due to both masses:$\frac{Gm}{x^2} = \frac{G(4m)}{(r-x)^2}$Taking the square root on both sides:$\frac{1}{x} = \frac{2}{r-x}$$r - x = 2x \implies 3x = r \implies x = \frac{r}{3}$Now,calculate the gravitational potential $V$ at point $P$:$V = -\frac{Gm}{x} - \frac{G(4m)}{r-x}$Substituting $x = \frac{r}{3}$ and $r-x = \frac{2r}{3}$:$V = -\frac{Gm}{r/3} - \frac{4Gm}{2r/3} = -\frac{3Gm}{r} - \frac{6Gm}{r} = -\frac{9Gm}{r}$

Two bodies of masses $m$ and $4m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them where the gravitational field is zero is

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