Question

The circle's radius in Case A is twice that of Case B. The period (time for one circle) in Case A is three times that of Case B. How does the speed in Case A compare to the speed in Case B? The speed in Case A is __________ .

A) The speed in Case A is half the speed in Case B.
B) The speed in Case A is the same as the speed in Case B.
C) The speed in Case A is twice the speed in Case B.
D) The speed in Case A is three times the speed in Case B.
E) The speed in Case A is six times the speed in Case B.

Answer 1

The speed in Case A is the same as the speed in Case B because the factors concerning radius and period cancel each other out.

Step-by-step explanation:

The question concerns the comparison of the speed of an object in two different cases of circular motion (Case A and Case B) with differing radii and periods. According to the information provided, the circle's radius in Case A is twice that of Case B, and the period in Case A is three times that of Case B. The measure of speed (velocity) in circular motion is calculated by dividing the circumference of the circle by the period (T). Since the circumference of a circle is proportional to its radius (C = 2πr), the circumference in Case A is twice that of Case B. However, due to the period in Case A being three times that in Case B, the speed in Case A (uA = 2πrA/TA) is the same as in Case B (uB = 2πrB/TB), because the factor of 2 from the larger radius cancels out with a third of the period.

Therefore, the correct response is B) The speed in Case A is the same as the speed in Case B.