Answer:
0.60 N, towards the centre of the circle
Explanation:
The tension in the string acts as centripetal force to keep the ball in uniform circular motion. So we can write:
[tex]T=m\omega^2 r[/tex] (1)
where
T is the tension
m = 0.015 kg is the mass of the ball
[tex]\omega[/tex] is the angular speed
r = 0.50 m is the radius of the circle
We know that the period of the ball is T = 0.70 s, so we can find the angular speed:
[tex]\omega=\frac{2\pi}{T}=\frac{2\pi}{0.70 s}=8.98 rad/s[/tex]
And by substituting into (1), we find the tension in the string:
[tex]T=(0.015 kg)(8.98 rad/s)^2(0.50 m)=0.60 N[/tex]
And in an uniform circular motion, the centripetal force always points towards the centre of the circle, so in this case the tension points towards the centre of the circle.
