A moving body with mass ' m ₁ ' strikes a stationary mass ' m₂ '. What should be the ratio m₁ m₂ so as to decrease the velocity of first by (1.5) times the velocity after the collision?

Step-by-step solution

Let initial velocity of mass m₁ be v₁ and final velocity of mass m₂ be v₂ According to the given condition, Final velocity of mass m ₁ is v ₁ 1.5 = 2 3 v ₁ Coefficient of restitution, e = Velocity after collision Velocity before collision array ll 1 & 1= (v₂- 2 v₁ 3 ) v₁ (e=1, for elastic collision ) & v₂= 5 v₁ 3 ...(i) array By following conservation of momentum aligned & m ₁ v ₁= m ₁ v ₁ 1.5 + m ₂ v ₂ & ~m ₁ v ₁= m ₁ 2 3 v ₁+ m ₂ 5 3 v ₁ & 1 3 ~m ₁ v ₁= m ₂ 5 3 v ₁ ~m ₁ ~m ₂ = 5 1 aligned