Question

Two particles $A$ and $B$ (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant when the speed of $A$ is $v$ and the speed of $B$ is $2v$, the speed of the centre of mass is

• A. Zero
• B. $v$
• C. $\frac{3v}{2}$
• D. $-\frac{3v}{2}$

Answer 1

The correct option is A Zero

Here $F_{ext}=0$, hence momentum will remain constant.

$p_i=p_f$

$0=m_a{v}_a+m_b{v}_b$ ( $p_i=0$ since both were at rest initially)

$0=m_a\times v-m_b\times 2v$

$m_b=\frac{m_a}{2}$

Now $V_{cm}=\frac{m_a{v}_a+m_b{v}_b}{m_a+m_b}$

Here $v_a=v$ and $v_b=-2v$

$V_{cm}=\frac{m_a\times v-\frac{m_a}{2}\times 2v}{m_a+\frac{m_a}{2}}$

$V_{cm}=0$