Solve this :

9. A uniform cylinder rolls from rest down the side of a trough given by y = x². The cylinder does not slip from A to B but the surface of the through is frictionless from B to C as shown. If the cylinder ascends up to C, then (Neglect the radius of cylinder).

$$\begin{gathered} \left(\mathrm{a}\right) {\mathrm{y}}_2={\mathrm{y}}_1 \left(\mathrm{b}\right) {\mathrm{y}}_2=\frac{2}{3}{\mathrm{y}}_1 \\ \left(\mathrm{c}\right) {\mathrm{y}}_2=\frac{{\mathrm{y}}_1}{3} \left(\mathrm{d}\right) {\mathrm{y}}_2=\frac{2}{5}{\mathrm{y}}_1 \end{gathered}$$