Answer:
d = 2.45 meters
Explanation:
Mass of the ball, m = 0.5 kg
Radius of the circle, r = 0.16 m
The angular speed of the ball around the circle is, [tex]\omega=2\ rad/s[/tex]
The attached figure shows the whole scenario. Let [tex]F_t[/tex] is the force acting on the ball in tangential direction. The forces will balanced each other at equilibrium.
In horizontal direction,
[tex]T\ sin\theta=F_t=mr\omega^2[/tex]................(1)
In vertical direction,
[tex]T\ cos\theta=mg[/tex]...............(2)
From equation (1) and (2) :
[tex]tan\theta=\dfrac{r\omega^2}{g}[/tex]
Also,
[tex]tan\theta=\dfrac{r}{d}[/tex]
[tex]d=\dfrac{g}{\omega^2}
[/tex][tex]d=\dfrac{9.8}{2^2}[/tex]
d = 2.45 meters
So, the value of d is 2.45 meters. Hence, this is the required solution.
