Question

A particle of mass m₁ makes an elastic, one-dimensional collision with a stationary particle of mass m₂. What fraction of the kinetic energy of m₁ is carried away by m₂?

(a) m₁ /m₂

(b) m₃ /m₁

(c) 2m₁m₂ / (m₁ + m₂)²

(d) 4m₁m₂ / (m₁ + m₂)²

Answer 1

Correct answer is: (d) 4m₁m₂ / (m₁ + m₂)²

Let v₁ and v₂ be the velocities of m₁ and m₂ after collision. Then,

m₁u = m₁v₁ + m₂v₂ and v₂ - v₁ = -1(0 - u)

Find v₂ in terms of u. The required fraction is