Question

A particle of mass m moving with a velocity v collides with a particle of mass 2m at rest and sticks to it. Velocity of the combined mass equal to? 

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

Answer 1

The Correct Option is C

To solve this problem, we apply the principle of conservation of linear momentum. When two particles collide and stick together, the total momentum before collision is equal to the total momentum after collision. Let's go through the solution step-by-step:

1. Understand the initial conditions:
   • Particle 1 (mass \(m\)) is moving with velocity \(v\).
   • Particle 2 (mass \(2m\)) is at rest, meaning its velocity is \(0\).
2. Calculate the initial momentum:
   • The initial momentum of particle 1 is given by: \(p_1 = m \cdot v\)
   • The initial momentum of particle 2 is given by: \(p_2 = 2m \cdot 0 = 0\)
   • Thus, the total initial momentum of the system is: \(P_{initial} = m \cdot v + 0 = m \cdot v\)
3. Apply conservation of momentum:
   • After collision, both particles stick together, forming a single particle with a combined mass of \(3m\).
   • Let the velocity of the combined mass be \(V\).
   • The final momentum is given by: \(P_{final} = (m + 2m) \cdot V = 3m \cdot V\)
   • According to the conservation of momentum: \(m \cdot v = 3m \cdot V\)
4. Solve for the velocity \(V\):
   • By dividing both sides by \(3m\): \(V = \frac{m \cdot v}{3m} = \frac{v}{3}\)
5. Conclusion:
   • The velocity of the combined mass after the collision is \(\frac{v}{3}\).

Therefore, the correct answer is \(\frac{v}{3}\).