The work required to bring the sphere to stop is equal to the kinetic energy possessed by the sphere.
Kinetic energy of a rotating body is given by,
K.E = [tex] \frac{1}{2}Iw^{2} [/tex]
Here, I= Moment of inertia of hollow sphere,
Since, the hollow sphere is rotating about the axis passing through its center, I =[tex] \frac{2}{3}MR^{2} [/tex]
M= Mass of the sphere= 3.8 kg,
R= Radius of gyration= Radius of the sphere= 0.25 m
w= Angular speed of the sphere = 13 rad/s
Substituting the values,
Kinetic energy =[tex] \frac{1}{2} *\frac{2}{3} (3.8)(0.25)^{2}(13.0)^{2} [/tex]
= 13.4 J
∴ Work required to bring the sphere to stop is 13.4 J.
