Question

Two masses $m$ and $m_x$ at infinite distance between them and initially at rest, start interacting gravitationally. The velocity of centre of mass when they are at a distance $S$ apart from each other is

• A. $\sqrt{\frac{4Gm}{S}}$
• B. $\sqrt{\frac{G{m}_x}{S}}$
• C. $\sqrt{\frac{2G{m}_x}{S}}$
• D. Zero

Answer 1

The correct option is D Zero

Given,

Both the masses are at rest initially, i.e($a_{cm\left(i\right)}=0,v_{cm\left(i\right)}=0$)

Now when they are at S distance apart,

Taking both masses as a system, $\text{no external force acts on them}$ during the motion from $\infty$ to $S$.

$\text{Note}$- Here mutual gravitational force will be internal in the system of both masses.

$F=m{a}_{cm\left(f\right)}=0$

$a_{cm\left(f\right)}=0$

$v_{cm\left(f\right)}=0+a_{cm\left(f\right)}t=0$

Hence $v_{cm\left(f\right)}=0$

Hence $\text{D}$ is the correct option.