Question

The small mass m sliding without friction along the looped track shown in figure 1 is to remain on the track at all times, even at the very top of the loop of radius r. What condition must be satisfied for the mass to remain on the track?

1) The centripetal force must be greater than or equal to the gravitational force.
2) The centripetal force must be less than or equal to the gravitational force.
3) The centripetal force must be equal to the gravitational force.
4) The centripetal force is not relevant in this situation.

Answer 1

The mass m must experience a centripetal force greater than or equal to the gravitational force at the top of the loop to remain on the frictionless track.

Step-by-step explanation:

To ensure that a small mass m remains on a frictionless looped track at all times, even at the top of the loop of radius r, a specific condition related to the forces on the mass must be satisfied. At the top of the loop, the centripetal force must be great enough to counteract the gravitational force pulling the mass downward. This condition can be stated as: the centripetal force must be greater than or equal to the gravitational force on the mass m at the top of the loop.

If this condition is not met, the mass will not have sufficient force to keep it moving in a circular path, leading to the mass leaving the track. Given the provided options for this question, the correct statement is that the centripetal force must be greater than or equal to the gravitational force (Option 1).