A sphere A moving with a speed ‘U’ and rotating with an angualr velocity ’$\mathrm{\omega }$’ makes head-on elastic collision with an identical stationary sphere. There is no friction between the surfaces A and B neglect gravity
A) A will stop moving but continue to rotate with angular velocity ’$\mathrm{\omega }$’.
B) A will come to rest and stop rotating
C) B will move with speed ‘U’ without rotating
D) B will move with speed U and rotate with an angular velocity w.

• When two identical particles collide head-on in an elastic collision, their velocities are switched after the collision, with A coming to rest and B moving with velocity u.
• The change in the rotational motion of the spheres is caused by friction force between their surfaces, which generates the requisite torque. 
• As a result, A will continue to rotate with angular velocity w while B does not rotate since there is no friction between the surfaces of A and B, causing them to complete the same rotation as when they first started.

Hence the correct answer is A & C.