Aball is attached to the end of a string. it is swung in a vertical circle of radius 1.5 m. what is the minimum velocity that the ball must have to make it around the circle?

Minimum velocity =8.57

Explanation:

To just complete vertical circular motion ball must cross the topmost point of circle with non zero tension.

So at topmost point make free body diagram showing all forces on ball.

For minimum velocity  make tension zero at top point

  =mg

⇒ v=

Now do mechanical energy conservation as work done by tension is zero all the way

Let initial velocity be v

v =

Now plug in the values

v=

v= 8.57