A solid sphere is rolling on a frictionless plane surface about the axis of symmetry. Find the rotational energy of the sphere. Also, find the ratio of rotational `K.E.` to total energy.

Explanation

Rot K.E. `=1/2 Iomega^(2) = 1/2 xx 2/5 MR^(2) xx V^(2)/R^(2)`
(As `omega = V/R, I = 2/5 MR^(2)`)
`=1/5 mv^(2)`
Total energy = Translation K.E. + Rot. K.E.
`=1/2mv^(2) + 1/5 mv^(2) = 7/10 mv^(2)`
`therefore ("Rot. K.E.")/("Total Energy") =(1/5 mv^(2))/(7/10 mv^(2)) = 2/7`