The correct answer is: E. All the above
- A. If two equal and perfectly elastic smooth spheres impinge directly, they interchange their velocities.
This is true because the total momentum of the system is conserved. The momentum of a moving object is its mass times its velocity. When two objects collide, the total momentum of the system before the collision must equal the total momentum of the system after the collision. If the two objects are equal in mass and perfectly elastic, then they will both move in the opposite direction after the collision, with the same speed as they were moving before the collision.
- B. If a sphere impinges directly on an equal sphere which is at rest, then a fraction $\frac{1}{2}\left( {1 – {{\text{e}}^2}} \right)$ the original kinetic energy is lost by the impact.
This is true because the coefficient of restitution, $e$, is a measure of how much energy is lost in an elastic collision. If $e=1$, then the collision is perfectly elastic and no energy is lost. If $e<1$, then some energy is lost in the collision. The fraction of energy lost is given by the equation $\frac{1}{2}\left( {1 – {{\text{e}}^2}} \right)$.
- C. If a smooth sphere impinges on another sphere, which is at rest, the latter will move along the line of centres.
This is true because the line of centers is the line that passes through the centers of the two spheres. When the two spheres collide, they will exert a force on each other that is perpendicular to the line of centers. This force will cause the spheres to rotate about their centers, and the sphere that is at rest will start to move along the line of centers.
- D. If two equal spheres which are perfectly elastic impinge at right angles, their direction after impact will still be at right angles.
This is true because the total momentum of the system is conserved. The momentum of a moving object is its mass times its velocity. When two objects collide, the total momentum of the system before the collision must equal the total momentum of the system after the collision. If the two objects are equal in mass and perfectly elastic, then they will both move in the opposite direction after the collision, with the same speed as they were moving before the collision. The direction of motion of the two objects will not change after the collision, because the total momentum of the system is still conserved.