Answer:
35.1688 seconds
Explanation:
M = Mass of sphere = 8200 kg
R = Radius of sphere = 90 cm
F = Force = 30 N
Moment of inertia is given by
[tex]I=\dfrac{2}{5}MR^2\\\Rightarrow I=\dfrac{2}{5}\times 8200\times 0.9^2\\\Rightarrow I=2656.8\ kgm^2[/tex]
Torque is given by
[tex]\tau=I\alpha\\\Rightarrow FR=I\alpha\\\Rightarrow \alpha=\dfrac{FR}{I}\\\Rightarrow \alpha=\dfrac{30\times 0.9}{2656.8}\\\Rightarrow \alpha=0.01016\ rad/s^2[/tex]
For one rotation
[tex]\theta=\omega_it+\dfrac{1}{2}\alpha t^2\\\Rightarrow 2\pi=0\times t+\dfrac{1}{2}\times 0.01016\times t^2\\\Rightarrow t=\sqrt{\dfrac{2\pi2}{0.01016}}\\\Rightarrow t=35.1688\ s[/tex]
The time taken to rotate the sphere from rest is 35.1688 seconds
