Question

Two particles of mass $m_1$ and $m_2$ are approaching towards each other under their mutual gravitational field. If the speed of the particle is $v$, the speed of the center of mass of the system is equal to:

• A. $\frac{m_1}{m_2}v$
• B. zero
• C. $\frac{(m_1-m_2)v}{m_1+m_2}$
• D. $\frac{m_2}{m_1}v$

Answer 1

Answer: (B)

zero

Taking both particles as a system,

$F_{ext}=0$

as mutual gravitational force becomes internal force here.

$a_{cm}=\frac{F_{ext}}{m}=0$

$v_{cm}=u_{cm}+a_{cm}t$

$v_{cm}=0$

$u_{cm}$ of system is zero as system starts from rest.

Hence v_{cm}=0$

Option $\text{B}$ is the correct answer.