Question

A 10 kg ball is swung in a horizontal circle at the end of a 2 - m rope over a persons head. The ball makes 30 revolutions per minute. How much time does it take for the ball to go around once and what is the speed of the ball?

Answer 1

Answer : T = 2 s and Speed = 6.28 m/s.

Explanation :

It is given that,

Mass of the ball, m = 10 kg

Radius of the circle, r = 2 m

The ball makes 30 revolutions per minute. So, frequency is given by :

$f=\dfrac{30}{60\ s}$

$f=\dfrac{1}{2}\ Hz$

We know that time period is defined as the reciprocal of frequency i.e.

$T=\dfrac{1}{f}$

$T=2\ s$

So, the time period for the ball to go around once is 2 s.

Now, speed is defined as distance travelled per unit time. Distance travelled by ball in circular path is equal to the circumference of the circle.

$Speed =\dfrac{distance}{time}$

$S=\dfrac{2\pi r}{T}$

$S=\dfrac{2\times 3.14\times 2\ m}{2\ s}$

$S=6.28\ m/s$

Speed of the ball is 6.28 m/s.