Elastic And Inelastic Collisions

To solve the problem, we need to determine the fraction of energy lost by body A after a head-on elastic collision with body B. Let's approach this step by step:

1. Before the collision, body A has a mass of and moves with a speed . Body B has a mass of and is initially at rest. The initial kinetic energies are:
   • Kinetic energy of A:
   • Kinetic energy of B: (as B is at rest)
2. In a head-on elastic collision, both momentum and kinetic energy are conserved. Conservation of momentum gives: 4mu = 4mv + 2mv_b\) , where and are the final velocities of A and B, respectively.
3. Conservation of kinetic energy gives:
4. From the conservation equations, the final velocity expressions for A and B in an elastic collision are:
5. The final kinetic energy of A is:
6. The energy lost by A can be calculated as the initial energy minus the final energy: 2mu^2 - \frac{2}{9}mu^2 = \frac{16}{9}mu^2\)
7. Thus, the fraction of energy lost by A is:

Thus, the fraction of energy lost by the colliding body A is , which matches the correct answer.