Question

Two spheres of mass $m$ and $M$ of the same radius $R$, are separated by a distance $\sqrt{8}R$. The force of attraction between them is:

• A. $\frac{2\sqrt{2}GmM}{27R^2}$
• B. $\frac{GmM}{8R^2}$
• C. $\frac{GmM}{9R^2}$
• D. $\frac{\sqrt{2}GmM}{9R^2}$

Answer 1

The correct option is B $\frac{GmM}{8R^2}$

A spherical mass behaves identical to a point mass placed at its centre. So, the system can be visualized as a system of two point masses m and M which are separated by a distance of $\sqrt{8}R$.

The force of attraction is:
$F=\frac{GMm}{(\sqrt{8}R{)}^2}$
$F=\frac{GMm}{8R^2}$