When the weight of a ball inside the ball mill is just balanced by the centrifugal force,

ANS:A - the ball abandons its circular path for a parabolic path.

the statement "the ball abandons its circular path for a parabolic path" is not accurate in the context of a ball mill or similar rotating systems. In a ball mill, the balls inside the mill are subjected to two main forces:

1. Centrifugal Force: This force pushes the balls outward against the inner surface of the mill due to the rotation of the mill. It is responsible for keeping the balls in motion along a circular path.
2. Gravity: This force acts downward, trying to pull the balls toward the bottom of the mill.

When the weight of a ball inside the ball mill is just balanced by the centrifugal force, it means that the centrifugal force is exactly counteracting the gravitational force acting on the ball. This equilibrium condition ensures that the ball remains in motion along a circular path without falling to the bottom of the mill. At no point does the ball abandon its circular path for a parabolic path in this scenario. The circular motion of the ball is maintained as long as the centrifugal force remains balanced by the gravitational force. Therefore, the statement "the ball abandons its circular path for a parabolic path" is not applicable to the behavior of balls inside a ball mill.