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 :
[tex]f=\dfrac{30}{60\ s}[/tex]
[tex]f=\dfrac{1}{2}\ Hz[/tex]
We know that time period is defined as the reciprocal of frequency i.e.
[tex]T=\dfrac{1}{f}[/tex]
[tex]T=2\ s[/tex]
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.
[tex]Speed =\dfrac{distance}{time}[/tex]
[tex]S=\dfrac{2\pi r}{T}[/tex]
[tex]S=\dfrac{2\times 3.14\times 2\ m}{2\ s}[/tex]
[tex]S=6.28\ m/s[/tex]
Speed of the ball is 6.28 m/s.
