Question

Two particles $A$ and $B$ of mass $1\text{kg}$ and $2\text{kg}$ are moving with velocity $u_A=10\text{m/s}$ and $u_B=20\text{m/s}$ respectively in opposite direction as shown in the figure. Find the magnitude of velocity of the centre of mass of the system.

• A. $10\text{m/s}$
• B. $15\text{m/s}$
• C. $5\text{m/s}$
• D. $20\text{m/s}$
  

Answer 1

The correct option is A $10\text{m/s}$

Given masses $m_A=1\text{kg},m_B=2\text{kg}$
velocity of mass $A$, $u_A=10\text{m/s}$
velocity of mass B, $u_B=-20\text{m/s}$
$\Rightarrow$velocity of system's $\text{COM}$ is given by:
$u_{\text{CM}}=\frac{m_A{u}_A+m_B{u}_B}{m_A+m_B}=\frac{1\left(10\right)+2(-20)}{1+2}$
$\therefore u_{\text{CM}}=\frac{-30}{3}=-10\text{m/s}$
Hence, velocity of $\text{COM}$ of system is $10\text{m/s}$ in the $-vex$ direction.