A uniform cylinder rolls down from rest,...

A uniform cylinder rolls down from rest, on a track whose vertical cross - section is a parabola given by the equation `y=kx^(2)`. If the surface is rough from A to B due to which the cylinder doesn't slip but it is frictionless from B to C, then the height of ascent of cylinder towards C is

`(y_(1))/(3)`

`(2y_(1))/(3)`

`(3y_(1))/(2)`

`y_(1)`

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