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A cylinder of mass 10 kg and radius 15 c...

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 ?

Text Solution

Verified by Experts

`M=10 kgm r=15 cm, mu_(s)=0.25`
force of friction `=(1)/(3) Mg sin theta`
`=(1)/(3)xx10xx9. 8 sin 30^(@)`
`=(1)/(3)xx10xx9.8xx(1)/(2)=16.33 N`
During rolling, the velocity at the point of contact is zero. Work done against friction will be zero For rolling without slipping,
`mu=(1)/(3) tan theta`
`rArr tan theta=3 mu=3xx0.25=0.75`
`:. theta=36.86^(@)`
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