Thank you for the opportunity to help you with your question!
Here how to solve this problem
You are given the mass of the ball and the distance. First, you need to find the radius, r of the circle that the ball is rotating around.
The equation for finding the velocity of the ball in circular movement is
v = 2*Pi * r/ T
The equation for the period, T is T = 2*Pi*r/ V
So you need to solve for the radius. The ball is hanging in the thread and rotating like a cone shape. So you need to find the radius, r of the cone. You are given the height, h= 1.9m of the cone. The equation to find the r of the cone is
r = h * tan( 32 degree)
r = 1.9 * (0.624)
= 1.18 m
To find the velocity, use this equation
v = (g*r)^2
= (9.8 m/s^2 * 1.18m)^2
= 3.4 m/s
So the speed of the ball in circular motion is 3.4 m/s
Let answer the second question of how long it takes , Tperiod for the ball to rotate once around the axis.
Tperiod = 2 Pi * r/ V
= (2 * 3.14* 1.18m) / 3.4 m/s
= 2.18 s
Please let me know if you need any clarification. I'm always happy to answer your questions.