Question

A ball is tied to the end of a cable of negligible mass. The ball is spun in a circle with a radius 2.00 m making 7.00 revolutions every 10.0 seconds. What is the magnitude of the acceleration of the ball?

1 : 67.9 m/s2

2 : 38.7 m/s2

3 : 29.3 m/s2

4 : 14.8 m/s2

5 : 74.2 m/s2

Answer 1

The acceleration of the ball will be

$$a=\omega^2 r=(2\pi n)^2r=\\\space\\=\bigg(2\pi \frac{N}{T}\bigg)^2r=\bigg(2\pi\frac{7}{10}\bigg)^2\cdot2=38.7\text{ m/s}^2.$$