A solid cylinder is placed on the end of an inclined plane. It is found that the plane can be tipped at an angle theta before the cylinder starts to slide. When the cylinder turns on its sides and is allowed to roll, it is found that the steepest angle at which the cylinder performs pure rolling is phi. The ratio tanphi//tantheta is

A solid cylinder is placed on the end of an inclined plane. It is foun

1.	A solid cylinder is placed on the end of an inclined plane. It is found that the plane can be tipped at an angle theta before the cylinder starts to slide. When the cylinder turns on its sides and is allowed to roll, it is found that the steepest angle at which the cylinder performs pure rolling is phi. The ratio tanphi//tantheta is
Answer» `3` `1/3` `1` `1/2` Solution :`f=Mgsintheta` for no SLIDING `fltf_(L)` `mgsintheta ltmu_(s)mgcostheta` `TANTHETA=mu_(s)` For rolling friction force `f=(mgsintheta)/(1+(R^(2))/(K^(2)))` `impliesf=(mgsinphi)/3` For pure rolling `(mgsinphi)/3ltmu_(s) mgcosphi` `tanphilt3mu_(s)` ,so `(tanphi)/(tantheta)=3`