Explanation:
The kinetic energy of translation
[tex]E_1=\frac{1}{2}mv^2[/tex]
m= mass v= linear velocity
The kinetic energy of rotation
[tex]E_2=\frac{1}{2}I\omega^2[/tex]
I= MOI of the thin walled sphere =kmR^2
where ω= v/R= angular velocity
[tex]E_2=\frac{1}{2}kmR^2\frac{v}{R}^2[/tex]
Then
[tex]\frac{E_1}{E_2} = \frac{0.5mv^2}{0.5kmR^2\frac{v}{R}^2 }[/tex]
=1/k
solid sphere: k=0.4; E1/E2 =1/0.4 = 2.5;
hollow sphere: k=2/3; E1/E2 = 1.5
