Question

A body B of mass m is at rest on a smooth horizontal surface. Another body A of equal mass moving with a velocity ‘u’ undergoes an oblique elastic collision with it. If v₁ and v₂ ; the velocities of A and B after collision make angle θ₁ and θ₂ with the original velocity u; then

(1) θ₁ + θ₂ = 180°

(2) θ₁ + θ₂ = 90°

(3) θ₁ + θ₂ = 120°

(4) θ₁ + θ₂ = 60°

Answer 1

(2) θ₁ + θ₂ = 90°

The bodies before and after collision are as shown in Fig. (a) & (b).

Total initial momentum of the system along X–axis before collision = mu + 0 = mu

Total final momentum of the system along X–axis after collision = m₁ v₁ cosθ₁ + m₂ v₂ cosθ₂

= mv₁ cosθ₁ mv₂ cosθ₂

By principle of momentum conservation.

Applying momentum conservation in y direction. We have