(A) PROVE THAT IN CASE OF OBLIQUE ELASTIC COLLISION OF TWO PARTICLES OF SAME MASS IF ONE IS AT REST, AFTER COLLISION BOTH PARTICLES MOVES AT RIGHT ANGLE TO EACH OTHER.
Consider two particles A and B of equal masses 'm'. Particle B collide with A obliquely by making an angle 'θ' with X-axis. After collision they move by making an angle Φ and α with x-axis. Refer to the following figure,
Using energy conservation:
Conservation of momentum:
So we have proved after collision particles get apart at perpendicular to each other.