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
`mgsinthetagtmumgcostheta`
or `tanthetagtmu`
the cylinder will topple if `(mgsintheta)(h)/(2)gt(mgcostheta)r`
or `tanthetagt(2r)/(h)` ..(ii)
thus thhe condiction of sliding in `tanthetagtmu` and condition of toppling is `tanthetagt(2r)/(h)` hence, the cylinder will slide before toppling if
`mult(2r)/(h)`
(b). The cylinder will topple before sliding if `mugt(2r)/(h)`