Two small bodies of masses $2.0~kg$ and $4.0~kg$ are kept at rest at a separation of $2.0~m$. Where

Question

Two small bodies of masses $2.0~kg$ and $4.0~kg$ are kept at rest at a separation of $2.0~m$. Where should a particle be placed on the line joining them to experience no net gravitational force?

Professor PC Thomas Classes · Answer

Let distance from $2~kg$ be $x$. $\frac{G(2)m}{x^2} = \frac{G(4)m}{(2-x)^2}$. Solving gives $\frac{\sqrt{2}}{x} = \frac{2}{2-x} \implies x = 2(\sqrt{2}-1) \approx 0.83~m$.