JEE Main2018PhysicsCenter of Mass, Momentum and CollisionActual
In a collinear collision, a particle with an initial speed v 0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50 % greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after the collision, is
Options
- Av 0 2
- Bv 0 4
- C2 v 0
- Dv 0 2
Correct answer
C. 2 v 0
Step-by-step solution
K E 2 = 3 2 m v 0 2 . Conservation of momentum, v 1 + v 2 = v 0 . Conservation of energy, 1 2 m v 1 2 + 1 2 m v 2 2 = 1 2 × 3 2 m v 0 2 ⇒ v 1 2 + v 2 2 = 3 2 v 0 2 ⇒ v 1 2 + v 2 2 + 2 v 1 v 2 = v 0 2 ⇒ 3 2 v 0 2 + 2 v 1 v 2 = v 0 2 ⇒ 2 v 1 v 2 = − 1 2 v 0 2 ⇒ ( v 1 − v 2 ) 2 = 3 2 v 0 2 + 1 2 v 0 2 = 2 v 0 2 ⇒ v 1 − v 2 = 2 v 0 .