Question

The gravitational force between two particles with masses m and M, initially at rest at great separation, pulls them together. When their separation becomes d, then speed of either particle relative to the other will be :

• A. $\sqrt{\frac{G(M+m)}{2d}}$
• B. $\sqrt{\frac{G(M+m)}{d}}$
• C. $\sqrt{\frac{2G(M+m)}{d}}$
• D. $\sqrt{\frac{4G(M+m)}{d}}$

Answer 1

The correct option is C

$\sqrt{\frac{2G(M+m)}{d}}$

By linear momentum conservation :

MV = mv .....(i)

By energy conservation

$0=-\frac{GMm}{d}+\frac{1}{2}M{V}^2+\frac{1}{2}m{v}^2$ .......(ii)

By solving (i) and (ii)

$V+v=\sqrt{\frac{2G(M+m)}{d}}$