It's a statics question, right? So you should be thinking, free body diagrams, sums of forces...Alexander Marks said:
The taut thread on a friction-less wire ring acts as a constraint, limiting the motion of the beads to a circular path along the ring. This means that the beads will always remain the same distance apart and will not deviate from the circular path.
In this system, there are two main forces acting on the beads: tension in the thread and the centripetal force. The tension in the thread keeps the beads from flying off the ring, while the centripetal force keeps them moving in a circular path.
The motion of the two beads is changing, as they are constantly accelerating towards the center of the ring due to the centripetal force. This results in a constant change in direction, even though the speed may remain constant.
The radius of the ring directly affects the motion of the beads. A smaller radius will result in a tighter circular path and a larger radius will result in a wider circular path. This will also affect the magnitude of the centripetal force acting on the beads.
Yes, the taut thread on the friction-less wire ring can be replaced with any other constraint that keeps the two beads at a fixed distance from each other and allows them to move in a circular path. This could include a rod, a string, or even a rigid bar.