A uniform of cylinder of height h and radius r is placed with its circular face on rough inclined plane and inclination of the plane to the horizontal is gradually increased. If µ is the coefficient of friction then

The cylinder will slide if   $\mathrm{mgsin}\mathrm{\theta }\ge \mathrm{\mu mgcos}\mathrm{\theta }\Rightarrow \tan \mathrm{\theta }>\mathrm{\mu }$
The cylinder will topple if $\mathrm{mgsin}\mathrm{\theta }\frac{\mathrm{h}}{2}>\mathrm{mgcos}\mathrm{\theta }.\mathrm{r}$
$\Rightarrow \tan \mathrm{\theta }>\frac{2\mathrm{r}}{\mathrm{h}}$
Condition for sliding $\tan \mathrm{\theta }>\mathrm{\mu }$
Condition for toppling is $\tan \mathrm{\theta }>\frac{2\mathrm{r}}{\mathrm{h}}$
Hence the cylinder will slide before toppling If $\mathrm{\mu }<\frac{2\mathrm{r}}{\mathrm{h}}$