A body of mass `M` and radius `r`, rolling on a smooth horizontal floor with velocity `v`, rolls up an irregular inclined plane up to a vertical height `(3v^(2)//4g)`. Compute the moment of inertia of the body.

Explanation

The total KE of the body
`K=K_(T)+K_(R )=(1)/(2)mv^(2)[1+(I)/(mr^(2))]`
When rolls up an inclined plane of height `h = (3V^(2))/(4g)` its KE is covereted into PE.
So `(1)/(2)mv^(2)[1+(I)/(mr^(2))]=mg((3v^(2))/(4g))` on simplification `I=(mr^(2))/(2)` hence the body is either a disc or cylinder.