On smooth incline $$ a=g \sin 30^{\circ} $$ by $\mathrm{S}=\mathrm{ut}+\frac{1}{2} \mathrm{at}{ }^2$ $$ \mathrm{S}=\frac{1}{2} \frac{\mathrm{~g}}{2} \mathrm{~T}^2=\frac{\mathrm{g}}{4} \mathrm{~T}^2 $$ On rough incline $$ a=g \sin 30^{\circ}-\mu g \cos 30^{\circ} $$ by $\mathrm{S}=\mathrm{ut}+\frac{1}{2} \mathrm{at}^2$ $$ S-{ }_4^1 g(1-\sqrt{3} \mu)(\alpha T)^2 $$ By (i) and (ii) $$ \begin{aligned} & \frac{1}{4} \mathrm{gT}^2=\frac{1}{4} \mathrm{~g}(1-\sqrt{3} \mu) \alpha^2 \mathrm{~T}^2 \\ & \Rightarrow \quad 1-\sqrt{3} \mathrm{~g}=\frac{1}{\alpha^2} \Rightarrow \mathrm{~g}=\left(\frac{\alpha^2-1}{\alpha^2}\right) \cdot \frac{1}{\sqrt{3}} \\ & \Rightarrow \mathrm{x}=3.00 \end{aligned} $$