\(K.E.\) of centre of mass when reached at bottom

\(=\frac{1}{2} M v^{2}+\frac{1}{2} I \omega^{2}=\frac{1}{2} M v^{2}+\frac{1}{2} M k^{2} v^{2} / R^{2}\)

\(=\frac{1}{2} M v^{2}\left(1+\frac{k^{2}}{R^{2}}\right)\)

For a solid cylinder \(\frac{k^{2}}{R^{2}}=\frac{1}{2}\)

\(\therefore \quad \mathrm{K.E.}=\frac{3}{4} M v^{2}\)

\(\therefore \quad M g h=\frac{3}{4} M v^{2}\)

\(v=\sqrt{\frac{4}{3} g h}\)