A stone is tied to a string and whirled at constant speed in a horizontal circle.The speed is then doubled without changing the length of the string.Afterward the magnitude of the acceleration of the stone is:
A)the same
B)twice as great
C)four times as great
D)half as great
E)one-fourth as great

Question

Quizplus · Accepted Answer

The magnitude of the acceleration of an object in uniform circular motion is given by a = v^2/r, where v is the linear speed of the object and r is the radius of the circle. Since the length of the string remains the same, the radius of the circle also remains the same. When the speed is doubled, the magnitude of the acceleration becomes a' = (2v)^2/r = 4(v^2/r). Therefore, the magnitude of the acceleration becomes four times as great.

A Stone Is Tied to a String and Whirled at Constant