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 y-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 maximum kinetic energy is lost.

Answer 1

The Correct Option is B

Step 1: Initial kinetic energy: Kᵢ = (1)/(2)m(2v)² + (1)/(2)(2m)v² Kᵢ = 2mv² + mv² = 3mv² Step 2: Total momentum before collision: vecp = (2mv)hati + (2mv)hatj Step 3: After perfectly inelastic collision, combined mass = 3m Velocity after collision: vf = frac√((2mv)² + (2mv)²)3m = \frac2√(2)3v Step 4: Final kinetic energy: Kf = (1)/(2)(3m)(\frac2√(2)3v)² = (4)/(3)mv² Step 5: Percentage loss in energy: % loss = (Kᵢ - Kf)/(Kᵢ) × 100 = (3 - (4)/(3))/(3) × 100 ≈ 62%