Question

Two identical balls are moving opposite to each other with the same speed. Which of the following is true if the collision is perfectly elastic? 
1. Both the balls comes to rest after collision
2. The balls recoil with the same speed after collision
3. The first ball comes to rest and the second ball moves along a different direction after collision
4. None of the above

Answer 1

Correct Answer - Option 2 : The balls recoil with the same speed after collision

The correct answer is option 2) i.e. The balls recoil with the same speed after the collision

CONCEPT:

• Elastic collision: Elastic collision is a phenomenon where the collision of objects takes place such that the total linear momentum and kinetic energy of the system are conserved.
• Collisions in one dimension:

​Let m1 and m2 be the masses of two objects that undergo elastic head-on collision. 

From the principle of momentum conservation,

⇒ m1v1i + m2v2i = m1v1f + m2v2f

where m1, m2 are the masses of the colliding bodies, v1i, v2i are the initial velocity and v1f and v2f are their final velocities.

​EXPLANATION:

Given that, m₁ = m₂ ; v_1i = v and v_2i = -v

Using, m1v1i + m2v2i = m1v1f + m2v2f

⇒ mv + m(-v) = mv1f + mv2f

⇒  0 = mv1f + mv2f

⇒  v1f  = -v2f

• Thus, the balls recoil at the same speed after the collision.