Question

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

• A. \(\frac{x}{3}\)
• B. \(\frac{x}{4}\)
• C. \(\frac{x}{8}\)
• D. \(\frac{x}{2}\)
• E. \(\frac{x}{5}\)

Hint:

Neutral point lies closer to smaller mass.

Answer 1

The Correct Option is A

Concept: Gravitational field: \[ g = \frac{GM}{r^2} \]

Step 1: Let point be at distance \(d\) from mass \(m\).
Distance from \(4m\) = \(x-d\)

Step 2: Equate fields.
\[ \frac{Gm}{d^2} = \frac{G(4m)}{(x-d)^2} \]

Step 3: Solve.
\[ \frac{1}{d^2} = \frac{4}{(x-d)^2} \Rightarrow \frac{1}{d} = \frac{2}{x-d} \] \[ x-d = 2d \Rightarrow x = 3d \Rightarrow d = \frac{x}{3} \]