Question

If a mass is tied to the end of a string and it goes around in a circular motion, will the tension do any work?

Answer 1

yup, it definitely does work. But the work done varies with displacement.
Suppose the object is at pt A initially and it is moving in clock-wise direction. Then, as it moves away from A and reaches the diametrically opposite pt B, its displacement keeps increasing and, thus, the work done increases. then as it completes the 2nd half of the circle, the displacement starts decreasing and so does the work done. And finally when it comes back to pt A, its displacement is 0 and so the work done = 0.
This cycle keeps on repeating. So, I'd say work done is a periodic function of displacement, or time, for that matter. since, after every time period, work done is 0.

Answer 2

Unfortunately tension does no work. Since tension as a force is always perpendicular to direction of displacement. \[Work = F.ds\] since tension is perpendicular so theta =90 so work done is 0

Answer 3

@Rdx.....yea, u're right. I forgot to take the directions into focus and just thought about the displacement. thanks!