Question

Ball A strikes with velocity $u$ elastically with identical ball B at rest, inclined at an angle of with line joining the centers of the two balls. What will be the speed of ball B after the collision?
A. $u$
B. $\dfrac{{u\sqrt 3 }}{2}$
C. $\dfrac{u}{2}$
D. $\dfrac{u}{{\sqrt 2 }}$

Answer 1

Recall the basic condition for the collision of the two objects. Recall the process of elastic collision of two objects when one of them is moving with some velocity and the other object is at rest. Hence, determine the speed of the ball B at rest after the elastic collision with the ball A.

Complete answer:
We have given that the ball A is moving with velocity $u$ and the ball B is at rest. For a ball B inclined at an angle with the line joining the centers of the two balls collision is not possible.

When an object moving with some velocity collides elastically with an object at rest, the moving object after collision stops and the object at rest starts moving with the same velocity as that of the object initially moving before the collision.

Hence, the ball B at rest will have the same speed $u$ as that of the ball A after the elastic collision along the lines joining the centers of these two balls. Therefore, the speed of the ball B after collision will be $u$.

Hence, the correct option is A.

Note: One should keep in mind that for the collision of two objects, the motion of the objects should be along the line joining the centers of the two objects. Otherwise, there will not be any collision between these two objects as the line joining their centers does not meet each other (which shows their paths of motion does not meet each other at any point for collision).