A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before collision i s _______ m s⁻¹.
Physics · Center of maas , Momentum and Collision · collision and types of collision
JEE Mains 25 January 2023 Shift 2 Evening Shift

Question

A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before collision i s _______ m s⁻¹.

Physics · Center of maas , Momentum and Collision · collision and types of collision

JEE Mains 25 January 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

Let the initial speed of the 1 kg body be u and the final speed of the 3 kg body be v. Momentum conservation gives u = -2 + 3v. For a one-dimensional elastic collision, relative speed of approach equals relative speed of separation: u = v + 2. Solving gives v = 2 m/s and u = 4 m/s.