A particle of mass $m$ moving with velocity $v$ collides with a stationary particle of mass $2 \mathrm{~m}$. After collision, they stick together and continue to move together with velocity

• A

  $\mathrm{v}$
• B

  $\frac{\mathrm{v}}{2}$
• Correct answer
  C

  $\frac{\mathrm{v}}{3}$
• D

  $\frac{v}{4}$

Solution

Applying conservation of linear momentum
$\Rightarrow \overrightarrow{\mathrm{P}}_{\mathrm{i}}=\overrightarrow{\mathrm{P}}_{\mathrm{f}}(\because \mathrm{P}=\mathrm{mv})$
$m v_1+2 m v_2=(m+2 m) v^{\prime}$
$m v^1+2 m \times 0=(3 m) v^{\prime}$
$\Rightarrow \mathrm{mv}=3 \mathrm{mv}^{\prime} \Rightarrow \mathrm{v}^{\prime}=\frac{\mathrm{v}}{3}$

Hence, the correct answer is option: 'C'.