Question

Two uniform solid spheres of equal radii $R$, but mass $M$ and $4 M$ have a center to center separation $6 R$ as shown.

If $N$ is the neutral point, then $r$ its distance from the centre of the sphere of mass $M$ is.

• A. $R$
• B. $\sqrt{2} R$
• C. $\sqrt{3} R$
• D. $2 R$

Answer 1

Answer: (D)

If a mass $m$ is kept at $N,$ the neutral point, then forces on it due to $M$ and $4 M$ balance.
$\frac{G M m}{r^{2}}=\frac{G(4 M) m}{(6 R-r)^{2}} \Rightarrow (6 R-r)^{2}=4 r^{2}$
$6 R-r=\pm 2 r$
$r=2 R$ or $r=-6 R$
$r$ is $+$ ve $,$ hence $r=2 R$