The following bodies,

$M g \sin \theta R=\left(m k^{2}+m R^{2}\right) \alpha$

$\alpha=\frac{\mathrm{Rg} \sin \theta}{\mathrm{k}^{2}+\mathrm{R}^{2}} \Rightarrow a=\frac{\mathrm{g} \sin \theta}{1+\frac{\mathrm{k}^{2}}{\mathrm{R}^{2}}}$

$t=\sqrt{\frac{2 s}{a}}=\sqrt{\frac{2 s}{g \sin \theta}\left(1+\frac{k^{2}}{R^{2}}\right)}$

for least time, $\mathrm{k}$ should be least \& we know $\mathrm{k}$ is least for solid sphere.