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 a) slide before toppingb) 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 a) slide before toppingb) topple before sliding
Answer» Solution : a) The CYLINDER will SLIDE if `MgsinthetagtmuMgcosthetaimpliestanthetagtmu.......(1)` The cylinder will topple if `(Mgsintheta)(h)/(2)gt(Mgcostheta)rimpliestanthetagt(2r)/(h).........(2)` THUS, the condition of sliding is `tanthetagtmu` and condition of TOPPLING `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)`