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

Solution

Physics sir · 3 steps

They stick together, so total momentum stays put while the mass triples: the speed must drop to a third.

1. Momentum is conserved. No external force acts during the collision, so total momentum before equals total momentum after. Kinetic energy is not conserved here, because the particles stick together.

   m v + 2m × 0 = (m + 2m) V

2. Solve for V. The left side is mv and the combined mass is 3m. So mv = 3mV, which gives V = v/3.
3. So. The two particles move together with velocity v/3, option (b).

The idea to keep. In a perfectly inelastic collision, use momentum only: common velocity = total momentum divided by total mass. Never use kinetic energy, because it is lost when bodies stick.

Answer from the NTA final answer key. Solution by PrepWiser.