A body of mass m moving with velocity v collides head-on elastically with another body of mass 2 m which is initially at rest. The ratio of K . E . of mass m before and after the collision will be

Step-by-step solution

K . E . of the colliding body before the collision = 1 2 m v 2 After collision its velocity becomes v ' = m 1 - m 2 m 1 + m 2 v = m 3 m v = v 3 ∴ K . E . after collision 1 2 m v ' 2 = 1 2 m v 2 9 The ratio of kinetic energy = K. E b e f o r e K.E after = 1 2 m v 2 1 2 m v 2 9 = 9 : 1