Suppose that she pushes on the sphere tangent to its surface with a steady force of F = 75 N and that the pressured water provides a frictionless support. How long will it take her to rotate the sphere one time, starting from rest?

The time taken to rotate the sphere one time is, t = 22 s

Explanation:

Given data,

The mass of the sphere, m = 8200 kg

The radius of the sphere, r = 90 cm

=.9 m

The force applied by the girl, F = 75 N

The moment of inertia of the sphere is,

I = 2/5 mr²

= (2/5) 8200 x (.9) ²

= 2657 kg·m²

The torque,

τ = I α

75 x 0.9 = 2657 x α

α = 0.0254 rad/s²

The angular displacement,

θ = ½αt²

2π = ½ x 0.0254 rad/s² x t²

t = 22 s

Hence, the time taken to rotate the sphere one time is, t = 22 s