In a glancing collision between two identical steel spheres, which of the follow

Question

In a glancing collision between two identical steel spheres, which of the following statements are correct?

(Assume this collision is perfectly elastic. Select all that apply.)

A) Kinetic energy in this collision will be conserved.

B) Linear momentum will be conserved in this collision.

C) The sum of the velocity vectors of the two spheres in the original direction of the incoming sphere after the collision will be equal to that of the incoming sphere.

D) The velocities of the spheres after the collision in the direction perpendicular to the incoming direction will be equal in magnitude and opposite in direction.

Explanation / Answer

A.) True. Energy is lost in an inelastic collision. But since it is given as perfectly elastic collision. Kinetic energy will be conserved.

B.) True. Linear moment will be conserved always as per the law of conservation of linear momentum.

C.) True. If v1 and v2 are the initial velocities of those identical spheres and v3 and v4 are the final velocities, according to the law of conservation of linear momentum mv1 + mv2 = mv3 + mv4

=> v1 + v2 = v3 + v4 this is because the spheres are identical and are having the same mass

D.)True. Because linear momentum should be conserved in all the directions even in the direction perpendicular to the direction of collision. So, before collision, the linear momentum was zero in the perpendicular direction, after collision, since the velocities are in the opposite direction with the same magnitude and since the mass is anyways same (identical spheres), the momentums of these two will cancel each other maintaining a zero linear momentum in the direction perpendicular to the direction of collision as before the collision.

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