Final answer:
The velocity of the ball moving in a circle with a diameter of 0.50 meters at 10 revolutions per second is 5π meters per second, or approximately 15.71 m/s.
Step-by-step explanation:
To calculate the velocity of the ball moving around a circle with a diameter of 0.50 meters at a rate of 10 revolutions per second, we use the formula for circular motion where the velocity v is the circumference of the path divided by the period of revolution (T). The circumference C of a circle is C = πd, where d is the diameter. Therefore, the ball covers a distance of C = π × 0.50 m in one revolution. Since it completes 10 revolutions per second, the period T is 0.1 seconds per revolution. The velocity v is then calculated as:
v = C/T = (π × 0.50 m) / 0.1 s
v = 5π m/s
Thus, the velocity of the ball is 5π meters per second, or approximately 15.71 m/s.