Answer :
Answer:
[tex]473.56\ \text{J}[/tex]
Explanation:
T = Time taken to complete one revolution = 0.3 s
m = Mass of sphere = 15 kg
r = Radius of sphere = 0.6 m
I = Moment of inertia of sphere = [tex]\dfrac{2}{5}mr^2[/tex]
Angular speed of the sphere is
[tex]\omega=\dfrac{2\pi}{T}=\dfrac{2\pi}{0.3}\\\Rightarrow \omega=20.94\ \text{rad/s}[/tex]
Rotational kinetic energy is given by
[tex]K_r=\dfrac{1}{2}I\omega^2=\dfrac{1}{2}\times \dfrac{2}{5}mr^2\omega^2\\\Rightarrow K_r=\dfrac{1}{2}\times \dfrac{2}{5}\times 15\times 0.6^2\times 20.94^2\\\Rightarrow K_r=473.56\ \text{J}[/tex]
The rotational kinetic energy of the sphere is [tex]473.56\ \text{J}[/tex].