A cylinder of mass `10 kg` and radius `15 cm` is rolling perfectly on a plane of inclination `30^(@)`. The coefficient of static friction is `mu_(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 `theta` of plane is increased, at what value of `theta` does the cylinder begin to skid and not roll perfectly ?

Explanation

(a) `f=(1)/(2)mg sin theta`
`=(1)/(3)xx10xx9.8xxsin 30^(@) N=16.3 N`.
(b) No work is done against friction during rolling.
(c ) `mu=(1)/(3)tan theta " or " tan theta=3 mu`
`tam theta=3xx0.25=0.75`
`theta=tan^(-1)(0.75)`
`=36.87^(@)=37^(@)`.