Portion `AB` of the wedge shown in figure is rough and `BC` is smooth. A solid cylinder rolld without slipping from `A` to `B`. Find the ratio of translational kinetic energy to rotationa linetic energy, when the cylinder reaches point `C`.
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Answer

`5`

Explanation

Up to point `B` solid cylinder rolls beyond `B` due to absence of friction and prence of `mg sin theta, omega` remains constant while `V_(CM)` remain constant
at point `B =(K_(R))/(K_(T)) = ((1)/(2) I omega^(2))/((1)/(2) mv^(2))`
`(K_(R))/(K_(T)) =((1)/(2) xx(1)/(2) mR^(2) xx((v)/(R))^(2))/((1)/(2) mv^(2))`
`(K_(R))/(K_(T)) =(1)/(2) rArr (K_(R))/(K_(T) + K_(R)) = (1)/(3)`

`(K_(R))_(B) = (1)/(3) mg ((h)/(2))` now `(K_(R))_(B) = (K_(R))_(C)`
`(K_(r))_(C) = mgh -(K_(R))_(C)`
`(K_(r))_(C) = (5)/(6) mgh rArr ((K_(T))_(C))/((K_(R))_(C)) = 5`.