Discussion
Two bodies of masses m and 4m are kept at a distance of x . The distance on the axial point from m at which the gravitational field is zero is
Answer: A
The field is zero at \(\frac{x}{3}\) from m.
Between the two masses the fields point in opposite directions. At distance d from m they balance when
\[ \begin{aligned} \frac{Gm}{d^{2}} &= \frac{G(4m)}{(x - d)^{2}} \\ x - d &= 2d \Rightarrow d = \frac{x}{3} \end{aligned} \]
The neutral point lies nearer the smaller mass. \(\frac{x}{2}\) would be the midpoint, correct only for equal masses, and \(\frac{x}{5}\) comes from equating \(m/d\) with \(4m/(x - d)\) without squaring.
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