A ball moves with a constant speed of 4 m/s around a circle of radius 0.25 m. What is the period of the motion? [Hint: For this calculation, you need to know the circumference of the circle.]
A)0.1 s
B)0.4 s
C)0.7 s
D)1 s
E)2 s

Question

Quizplus · Accepted Answer

The period, T, is the time it takes for the ball to complete one full revolution around the circle. The circumference of a circle is given by:

C = 2πr

where r is the radius. In this case, r = 0.25 m, so:

C = 2π(0.25) = 1.57 m

The speed of the ball is constant and equal to 4 m/s. We know that:

speed = distance/time

In this case, the distance traveled is equal to the circumference of the circle, and the time taken is equal to the period, T. So:

4 = 1.57/T

Multiplying both sides by T, we get:

T*4 = 1.57

Dividing both sides by 4, we get:

T = 0.39 s

So the period of the motion is 0.4 s, which is closest to choice (B).

A Ball Moves with a Constant Speed of 4 M/s