A sphere of mass m moving with a constant velocity u hits another stationary sphere of the same mass. If e is the coefficient of restitution, then the ratio of velocities of the two spheres after collision ( V₁ V₂ ) will be

Step-by-step solution

Conservation of momentum (gives) m u+0=m v₁+m v₂ v₁+v₂=u (i) Newton's experimental formula, v₁-v₂=-e [u₁-u₂ ] gives v₁-v₂=-e u (ii) From Eqs. (i) and (ii), we get v₁= (1-e) u 2 v₂= (1+e) u 2 V₁ V₂ = 1-e 1+e