Two identical balls A and B are released from the positions .They collide elastically on horizontal position MN. The ratio of the heights attained by A and B after collision will be ?
To determine the ratio of the heights attained by balls A and B after the collision, we need to consider the conservation of mechanical energy and momentum.
Let's denote the initial positions of balls A and B as A₀ and B₀ respectively. Since the balls are released from rest, they have no initial velocities.
1. Conservation of mechanical energy:
In an elastic collision, the total mechanical energy before and after the collision remains the same. Since both balls are released from the same position (height), their initial gravitational potential energy is the same.
Thus, the post-collision heights attained by balls A and B will depend solely on their individual masses. Let's denote the masses of the balls as mA and mB.
2. Conservation of momentum:
In an elastic collision, the total momentum before and after the collision also remains the same. The total momentum of system before the collision is zero because the balls are at rest.
After the collision, the system will still have zero total momentum since both balls have the same mass and they collide on a horizontal plane. Therefore, the final velocities of balls A and B will be equal in magnitude but opposite in direction.
In conclusion, the ratio of the heights attained by balls A and B after the collision will solely depend on their masses. If mA > mB, then the height attained by ball A will be greater than ball B. On the other hand, if mB > mA, then the height attained by ball B will be greater than ball A.
The ratio of heights attained (hA/hB) cannot be determined with the given information about the masses of the balls A and B.