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

Question

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, v 0 2, v 0 4, 2 v 0, v 0 2

MARKS App · Accepted Answer

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 .

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