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# 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

$(a)\;zero \quad (b)\;\frac{-4GM}{r} \quad (c)\;\frac{-6GM}{r} \quad (d)\;\frac{-9GM}{r}$

Let the point be the position when the gravitational field is zero
$\large\frac{Gm}{x^2}=\large\frac{G(4m)}{(r-x)^2}$
$\large\frac{1}{x}=\frac{2}{(r-x)}$
$r-x=2x$
$x=\large\frac{r}{3}$
the point P is at a distance $\large\frac{r}{3}$ from mass m and $\large\frac{2r}{3}$ from mass 4m
$V= \large\frac{-GM}{\Large\frac{r}{3}}-\frac{G(4m)}{\Large\frac{2r}{3}}$
$\quad= \large\frac{-9GM}{r}$
Hence d is the correct answer.
edited Jul 3, 2014