A ball of 0.1 kg makes an elastic head on collision with a ball of unknown mass that is initially at rest. If the 0.1 kg ball rebounds at one third of its original speed, what is the mass of the other ball? 

Here, m₁ = 0.1 kg,   m₂ = ?,   u₂ = 0

Let u₁ = u

∴ v₁ = −u / 3

As v₁ = [(m₁ − m₂)u₁ + 2m₂u₂] / (m₁ + m₂)

∴ −u / 3 = (0.1 − m₂)u / (0.1 + m₂)

or −1 / 3 = (0.1 − m₂) / (0.1 + m₂)

or −0.3 + 3m₂ = 0.1 + m₂

2m₂ = 0.1 + 0.3 = 0.4

∴ m₂ = 0.4 / 2 = 0.2 kg