Question

A particle of mass m moving in the x-direction with speed 2v is hit by another particle of mass 2m moving in the same direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

• A. 56%
• B. 62%
• C. 44%
• D. 50%

Hint:

In perfectly inelastic collisions, momentum is conserved but kinetic energy is not.

Answer 1

The Correct Option is D

Step 1: Initial kinetic energy Kᵢ = \tfrac12 m(2v)² + \tfrac12 (2m)v² = 3mv²
Step 2: Final velocity after perfectly inelastic collision vf = (2mv + 2mv)/(3m) = (4v)/(3)
Step 3: Final kinetic energy Kf = \tfrac12 (3m)((4v)/(3))² = (8)/(3)mv²
Step 4: Fractional loss (Kᵢ-Kf)/(Kᵢ) ≈ 0.5