If a spherical ball rolls on a table without slipping the friction of its total energy associated with rotational energy is :

Step-by-step solution

Rotational energy of sphere E_R= 1 2 I ^2 For sphere, moment of inertia aligned I & = 2 5 m R^2 E_R & = 1 2 ( 2 5 m R^2 ) ( v R )^2 & = 1 5 m v^2 aligned Translational kinetic energy E_r= 1 2 m v^2 aligned Total energy & = 1 5 m v^2+ 1 2 m v^2 & = 7 10 m v^2 aligned Required fraction = 1 5 m v^2 7 10 m v^2 = 2 7