When a body is under pure rolling, the fraction of its total kinetic energy which is the purely rotational is 2/5. Identify the body.

Explanation

In this type of questions calculate the expression for moment of inertia l and that helps in identify the body.
Rotational KE `= (1)/(2)l omega^(2)`
Translation KE `= (1)/(2) Mv^(2)`
`therefore` Total KE `= (1)/(2)l omega^(2)+(1)/(2)Mv^(2)`
Given `(2)/(5) = ("Rotationa KE")/("Total KE")`
or `(2)/(5)=((1)/(2)l omega^(2))/((1)/(2)l omega^(2)+(1)/(2)Mv^(2))`
For pure rolling put `v = omega R`
or `(2)/(5)=(l omega^(2))/(l omega^(2)+M omega^(2)R^(2))`
`therefore l = (2MR^(2))/(3)`
So, the rolling body is hollow sphere.