A uniform cylinder of height `h` and radius `r` is placed with its circular face on a rough inclined plane and the inclination of the plane to the horizontal is gradually increased. If `mu` is the coefficient of friction, then under what condition the cylinder will (a) slide before toppling (b) topple before sliding.

Explanation

(a) The Cylinder will slide if
`Mgsintheta gt mu Mgcosthetaimpliestantheta gt mu`……….`(1)`
The cylinder will topple if
`(Mgsintheta)(h)/(2) gt (Mg costheta)rimpliestantheta gt (2r)/(h)`…………`(2)`
Thus, the condition of sliding is `tantheta gt mu` and condition of toppling `tantheta gt (2r)/(h)`. Hence, the cylinder will slide before toppling if `mu lt (2r)/(h)`
(b) The cylinder will topple before sliding if `my gt (2r)/(h)`