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 gradually in creased. If mu is the coefficeint of friction, then under what conditions the cylinder will a) slide before topping b) topple before sliding

A uniform cylinder of height h and radius r is placed with its circula

1.	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 gradually in creased. If mu is the coefficeint of friction, then under what conditions the cylinder will a) slide before topping b) topple before sliding
Answer» Solution : (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)`