A mass `m` of radius `r` is rolling horizontally without any slip with a linear speed `v`. It then rolls up to a height given by `(3)/(4)(v^(2))/(g)`

Options

A. the body is identified to be a disc or a solid cylinder
B. the body is a solid sphere
C. moment of inertia of the body about instantaneous axis of rotation is `(3)/(2)mr^(2)`
D. moment of inertial of the body about instantaneous axis of rotation is `(7)/(5)mr^(2)`

Explanation

`(K_(R))/(K_(T))=(I)/(mr^(2))`
`thereforeK_(T)=((mr^(2))/(I+mr^(2)))K_("total")`
or `K_("total")=((I+mr^(2))/(mr^(2)))((1)/(2)mv^(2))`
`=mgh=mg((3)/(4)(v^(2))/(g))`
solving we get `I=(1)/(2)mr^(2)` so it is either solid cylinder or disc.