Question

A ball is whirled on the end of a string in a horizontal circle of radius R at constant speed v. (ac =v2/R)

Complete the following statement: When the radius R is decreased by a factor of 5, keeping the speed fixed, the centripetal acceleration
a. increases by a factor of 5.
b. decreases by a factor of 5.
c. remains the same.
d. decreases by a factor of 25.

Answer 1

Decreasing the radius by a factor of 5, while keeping the speed constant, increases the centripetal acceleration by a factor of 5 because centripetal acceleration is inversely proportional to the radius.

Step-by-step explanation:

When the radius R is decreased by a factor of 5 while keeping the speed fixed, the centripetal acceleration (ac = v^2/R) is affected in the following way: since ac is inversely proportional to the radius of the circle, it will increase when the radius is decreased. Specifically, if R is decreased by a factor of 5, the centripetal acceleration will increase by a factor of 5. However, it must be noted that the centripetal acceleration is also directly proportional to the square of the speed, v, so changes to speed can have a significant impact as well. In this case, the speed remains constant, so we only account for the change in the radius. Therefore, the correct answer is (a) increases by a factor of 5.