A body of mass m₁ collides elastically with another body of mass m₂ at rest. If the velocity of m₁ after collision becomes 2 / 3 times its initial velocity, the ratio of their masses is

Step-by-step solution

Let v be the initial velocity of body of mass m₁ before collision. Since collision is elastic both momentum and kinetic energy are conserved. m₁ v=m₁ 2 3 v+m₂ v₂ or m₁ (v- 2 3 v )=m₂ v₂ Also, 1 2 m₁ v^2= 1 2 m₁ ( 2 3 )^2 v^2+ 1 2 m₂ v₂^2 or m₁ (v^2- 4 9 v^2 )=m₂ v₂^2 or m₁ m₂ = 9 v₂^2 5 v^2 Equating (i) and (ii), we get aligned & 9 v₂^2 5 v^2 = 3 v₂ v or v₂ v = 5 3 & m₁ m₂ = 3 5 3 = 5 1 aligned