An object moves around a circle. If the radius is doubled keeping the speed the same then the magnitude of the contripetal force must be:
A) twice as great
B) half as great
C) four times as great
D) one-fourth as great
E) the same

Question

Quizplus · Accepted Answer

The formula for centripetal force is Fc = mv^2/r, where m is the mass of the object, v is its velocity, and r is the radius of the circle. Doubling the radius while keeping the speed constant means that the velocity v remains the same, but r is now 2r. Plugging these values into the formula, we get:

Fc = m(v^2)/(2r)

Notice that the denominator is now twice as large, but the numerator remains the same. Therefore, the magnitude of the centripetal force must be half as great as it was before. Therefore, choice B is correct.

An Object Moves Around a Circle