A solid cylinder rolls without slipping along a horizontal plane with velocity 66 m/s and reaches a plane inclined at  ${60}^0$ with the horizontal. If there is sufficient friction to prevent slipping then the body starts rolling up the inclined plane with the velocity v. Find the value of v(in m/s)

Initial angular momentum of the solid sphere about B
 $\Rightarrow I\omega +m{v}_{cm}r=\frac{m{R}^2}{2}\frac{V_C}{R}+m{v}_{C}R\cos \theta$
Final angular momentum of the solid sphere at  $B=mvR+\frac{m{R}^2}{2}\frac{v}{R}$
Angular momentum about the B will remain conservation $L_i=L_F$ 
 
 $$\begin{gathered} \frac{m{R}^2}{2}.\frac{v_C}{R}+m{v}_{C}R\cos {60}^0=mvR+\frac{m{R}^2}{2}\frac{v}{R} \\ 66\times \frac{R}{2}+66\times \frac{R}{2}=v\times R+\frac{vR}{2} \\ 66R=\frac{3vR}{2} \\ v=44m/\sec \end{gathered}$$
Angular momentum about B will then remain conserved