A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is

Step-by-step solution

Under pure rolling condition: v = ω R Translational K . E = 1 2 m v 2 Rotational K . E = 1 2 × 2 5 m R 2 v R 2 = 1 5 m v 2 Total K . E = 1 2 m v 2 + 1 5 m v 2 = 7 10 m v 2 So, Rotational   K · E Total   K · E = 1 5 m v 2 7 10 m v 2 = 2 7