Question

A particle of mass \( m \) moving with velocity \( v \) collides with a stationary particle of mass \( 2m \). After the collision, they stick together and continue to move with velocity:

• A. \( v \)
• B. \( \frac{v}{2} \)
• C. \( \frac{v}{3} \)
• D. \( \frac{v}{4} \)

Hint:

For completely inelastic collisions (when objects stick together after collision), use: \[ m_1 v_1 + m_2 v_2 = (m_1 + m_2) V_f \] where \( V_f \) is the common velocity after collision.

Answer 1

The Correct Option is C

Step 1: Applying the Law of Conservation of Momentum. The total momentum before collision is: \[ P_{{initial}} = m v + (2m \times 0) = m v \] Since the two masses stick together after collision, their combined mass is: \[ M = m + 2m = 3m \] Let the final velocity be \( V_f \). According to conservation of momentum: \[ m v = (3m) V_f \] Step 2: Solving for \( V_f \). \[ V_f = \frac{m v}{3m} = \frac{v}{3} \] Final Answer: \[ \boxed{\frac{v}{3}} \]