superposition principle

Question

Two masses m and 4m are placed at a distance d apart. At what point on the line joining them will the gravitational field intensity be zero?

RankGuru · Accepted Answer

1. **Goal**: Find distance $x$ from mass $m$ where the field from $m$ is canceled by the field from $4m$.
2. **Set up Balance**: $E_1 = E_2$.
   - $\frac{Gm}{x^2} = \frac{G(4m)}{(d-x)^2}$.
3. **Simplify Ratio**: $\frac{1}{x^2} = \frac{4}{(d-x)^2}$.
4. **Square Root Path**:
   - $\frac{1}{x} = \frac{2}{d-x}$
   - $d - x = 2x$
   - $d = 3x \implies x = d/3$.
5. **Conclusion**: The 'neutral point' is located at distance **$d/3$** from the lighter mass $m$.

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