Answer:
The angular velocity is 15.37 rad/s
Solution:
As per the question:

Horizontal distance, x = 30.1 m
Distance of the ball from the rotation axis is its radius, R = 1.15 m
Now,
To calculate the angular velocity:
Linear velocity, v = 
v = 
v = 
v = 
Now,
The angular velocity can be calculated as:

Thus

The magnetic force acting on a charged particle moving perpendicular to the field is:
= qvB
is the magnetic force, q is the particle charge, v is the particle velocity, and B is the magnetic field strength.
The centripetal force acting on a particle moving in a circular path is:
= mv²/r
is the centripetal force, m is the mass, v is the particle velocity, and r is the radius of the circular path.
If the magnetic force is acting as the centripetal force, set
equal to
and solve for B:
qvB = mv²/r
B = mv/(qr)
Given values:
m = 1.67×10⁻²⁷kg (proton mass)
v = 7.50×10⁷m/s
q = 1.60×10⁻¹⁹C (proton charge)
r = 0.800m
Plug these values in and solve for B:
B = (1.67×10⁻²⁷)(7.50×10⁷)/(1.60×10⁻¹⁹×0.800)
B = 0.979T
Use the equation potential energy =m*g*h
m-mass,
g-gravitational acceleration,
h-height
Potential energy = 2*10*10
=200

This is the unit of the energy