Question

Two bodies of masses of $1\text{kg}$ and $3\text{kg}$ initially at rest are moving with velocities $30\text{m/s}$ and $10\text{m/s}$ towards each other due to mutual force of attraction. What is the velocity of the centre of mass of system?

• A. $8\text{m/s}$
• B. $\text{Zero}$
• C. $2\text{m/s}$
• D. $4\text{m/s}$

Answer 1

The correct option is B $\text{Zero}$


Considering $+vex-$ direction along the velocity of $1\text{kg}$,
$m_1=1\text{kg},v_1=30\text{m/s},m_2=3\text{kg},v_2=-10\text{m/s}$
$\Rightarrow$Applying the formula for velocity of centre of mass of system:
$v_{\text{com}}=\frac{m_1{v}_1+m_2{v}_2}{m_1+m_2}$
$\Rightarrow v_{\text{com}}=\frac{(1\times 30)+(3\times (-10\left)\right)}{1+3}$
$\therefore v_{\text{com}}=0\text{m/s}$