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
`Mg sin theta gt mu Mg cos theta rArr tan theta gt mu` …..(1)
the cylinder will topple if
`(Mg sin theta) (h)/(2)gt (M g cos theta) r rArr tan theta gt (2r)/(h)` ...(2)
Thus, the condition of sliding is `tan theta gt mu` and condition of toppling `tan theta gt (2r)/(h)`. Hence, the cylinder will slide before toppling if `mu lt (2r)/(h)`
(b) The cylinder will topple before sliding if `mu gt (2r)/(h)`