Question

A ball of mass m moving with velocity V makes a head on elastic collision with a ball of the same mass moving with velocity 2V towards it. Taking direction of V as positive velocities of the two balls after collision are

A. -V and 2V
B. 2V and -V
C. V and -2V
D. -2V and V

Answer 1

After the head-on elastic collision between two balls of equal mass, one initially moving with velocity V and the other with velocity 2V in the opposite direction, they exchange their velocities due to conservation of momentum and kinetic energy. The velocities after the collision will be -2V and V, respectively. Option d is the answer.

Step-by-step explanation:

The student has described a scenario involving an elastic collision between two balls of equal mass where one ball is moving with a velocity V and the other with a velocity of 2V in the opposite direction. In an elastic collision of two objects with equal mass, where one of the objects is stationary, the moving object comes to rest while the stationary object moves with the velocity of the initial moving object. However, in this scenario, since both objects are moving towards each other, they simply exchange their velocities after the collision due to the conservation of momentum and kinetic energy in elastic collisions.

Therefore, the first ball will move with a velocity of -2V and the second ball will move with a velocity of V after the collision, as their velocities are exchanged.