A 0.25-kg ball attached to a string is rotating in a horizontal circle of radius 0.5 m. If the ball revolves twice every second, what is the tension in the string?
A)2 N
B)5 N
C)7 N
D)10 N
E)20 N

Question

Quizplus · Accepted Answer

The tension in the string provides the centripetal force needed to keep the ball moving in a circle. The centripetal force $ F_c $ is given by $ F_c = m \cdot \omega^2 \cdot r $, where $ m = 0.25 \, \text{kg} $, $ r = 0.5 \, \text{m} $, and $ \omega = 2\pi \cdot f $ with $ f = 2 \, \text{revolutions per second} $. Calculating $ \omega = 2\pi \cdot 2 = 4\pi \, \text{rad/s} $, then $ F_c = 0.25 \cdot (4\pi)^2 \cdot 0.5 = 20 \, \text{N} $. Thus, the tension is 20 N.

A 025-Kg Ball Attached to a String Is Rotating in a a Horizontal