Question

Two particles which are initially at rest, move towards each due to mutual attraction. If their speeds are $v$ and $2v$ at any instant, then the speed of centre of mass of the system will be

• A. $2v$
• B. $1.5v$
• C. $0$
• D. $v$

Answer 1

The correct option is C $0$

The figure shown below represents the velocity of particles moving under influence of attractive forces.

velocity of c.o.m is given by,
${\overrightarrow{v}}_{\text{com}}=\frac{m_1{\overrightarrow{v}}_1+m_2{\overrightarrow{v}}_2}{m_1+m_2}$
Since particles are starting from rest, in initial case:
${\overrightarrow{v}}_{c.o.m}=0$ and ${\overrightarrow{v}}_1={\overrightarrow{v}}_2=0$
As they starts moving towards each other under the influence of mutual attraction, taking both particles as system attractive forces become internal for the system.
$\Rightarrow {\overrightarrow{F}}_{\text{ext}}=0$
for the system of particles, applying newton's second law:
${\overrightarrow{F}}_{\text{ext}}=m{\overrightarrow{a}}_{\text{com}}$
Hence ${\overrightarrow{a}}_{\text{com}}=0$
$\Rightarrow {\overrightarrow{v}}_{\text{com}}=\text{constant}$
Therefore velocity of $\text{COM}$ will not change.
$\Rightarrow v_i=v_f=0$
Speed of $\text{COM}$ of the system at any instant will be Zero.