A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination 30o. The co- efficient of static friction `µ_(s) = 0.25`.
(a) How much is the force of friction acting on the cylinder ?
(b) What is the work done against friction during rolling ?
(c) If the inclination `θ` of the plane is increased, at what value of `θ` does the cylinder begin to skid, and not roll perfectly ?

Explanation

Mass of cylinder `m=10kg`
Radius of cylinder `r=15cm=0.15m`
Angle of inclination `theta=30^(@)`
Coefficient of static friction `mu_(S)=0.25`
(a) Frictional force exerted on the cylinder parallel to the surface of slope
`f=(1)/(3)mgsintheta`
`=(1)/(3)xx10xx9.8xxsin30^(@)`
`=(1)/(3)xx10xx9.8xx(1)/(2)`
`=16.3N`
(b) Frictional force exerted on the cylinder perpendicular to the surface of slope = work done against friction force during rolling
`W=frcos90^(@)`
`W=0`
(c ) Condition of rolling without sliding
`mu=(1)/(3)tantheta`
`therefore tantheta=3mu`
`=3xx0.25`
`=0.75`
`therefore theta=36^(@)54`
`therefore theta~~37^(@)`