91Ó°ÊÓ

Consider a head-on elastic collision between two bodies, A and B, with equal masses m_A = m_B = m and initial velocities u_A and u_B, respectively. In an elastic collision, both momentum and kinetic energy are conserved. Let the final velocities be v_A and v_B. The conservation of momentum equation is as follows: \(m_Au_A + m_Bu_B = m_Av_A + m_Bv_B\) Since the masses are equal, we have: \(mu_A + mu_B = mv_A + mv_B\) Dividing both sides by m, we get: \(u_A + u_B = v_A + v_B\) The conservation of kinetic energy equation is: \(\frac{1}{2}m_Au_A^2 + \frac{1}{2}m_Bu_B^2 = \frac{1}{2}m_Av_A^2 + \frac{1}{2}m_Bv_B^2\) As the masses are equal, we have: \(\frac{1}{2}mu_A^2 + \frac{1}{2}mu_B^2 = \frac{1}{2}mv_A^2 + \frac{1}{2}mv_B^2\) Dividing both sides by \(\frac{1}{2}m\), we get: \(u_A^2 + u_B^2 = v_A^2 + v_B^2\) By solving these two equations simultaneously, we find that the final velocities of the colliding bodies are interchanged: v_A = u_B and v_B = u_A. So, statement (A) is correct.

In an elastic collision, kinetic energy is conserved before the collision, during the collision, and after the collision. By definition, an elastic collision is one in which the total kinetic energy of the system is conserved. Therefore, statement (B) is correct.

The principle of conservation of momentum states that the total momentum of a closed system of particles remains constant if no external forces act on the system. In an elastic collision, momentum is conserved before, during, and after the collision, assuming that no other forces act on the system. Therefore, statement (C) is correct.

In an oblique elastic collision, bodies collide at an angle and not head-on. Even though the total momentum and kinetic energy are conserved in an oblique elastic collision, the velocities of the two bodies do not necessarily interchange. The final velocities depend on the angle between their initial velocities and the collision angle, which makes the outcome more complex. Therefore, statement (D) is incorrect. In conclusion, statements (A), (B), and (C) are correct, while statement (D) is incorrect.