What is the velocity of a ball swung around on a rope with
radius .25 meters and period .40 seconds? (write your answer
two significant figures. e. g. : 2.5)
/seconds

The velocity of ball swinging around the circular path on a rope is 1.4  m/s.

Given data:

The radius of swing is, r = 0.25 m.

The time period of swing is, T = 0.40 s.

In this problem, the ball is tied with rope to make it traverse along a circular path.

The expression for the velocity of ball swinging around the circular path along the rope is given as,

Here, C is the circumference traversed by the ball. And its value is,

Solving for velocity as,

Thus, the velocity of ball swinging around the circular path on a rope is 1.4  m/s.

Learn more about the time period around the circular path here:

link

3.9 m/s

Explanation:

The circumference of the circular path is:

C = 2πr

C = 2π (0.25 m)

C = 1.57 m

The speed is therefore:

v = C / t

v = (1.57 m) / (0.40 s)

v = 3.9 m/s