Question - 8 A 0.280-kg croquet ball makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first ball. What is the mass of the second ball

Mass of the second ball is 0.84 kg

Explanation:

The collision is said to be elastic collision when the kinetic energy of the system remains conserved after the balls collides. The momentum of the system is also conserved.

The mass of the first ball is m₁ = 0.280 kg

We have to the find the mass of second ball m₂.

Let

    initial velocity of first ball be u₁

   initial velocity of second ball is u₂ =0

   mass of second ball is m₂

   Final velocity of second ball is 0.5 u₁

As the collision is elastic

 u₂-u₁ = v₂-v₁

   0-u₁ =0.5 u₁-v₁

    v₁ = -0.5 u₁

According to law of conservation of momentum,

    m ₁u₁+m₂u₂=m₁v₁+m₂v₂

0.280*u₁+m₂*0=0.28* -0.5 u₁+m₂*0.5 u₁

0.28 u₁ +0.14 u₁  = 0.5u₁m₂

      m₂= 0.84 kg

The mass of the second ball is 0.84 kg.