PhysicsA cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination 300. The co-efficient of static friction μk=0.25. If the inclination θ of the plane is increased, at what value of θ does the cylinder begin to skid, and not roll perfectly?

A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination 300. The co-efficient of static friction μk=0.25. If the inclination θ of the plane is increased, at what value of θ does the cylinder begin to skid, and not roll perfectly?

  1. A

    37°

  2. B

    53°

  3. C

    90°

  4. D

    0°

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    Solution:

    The cylinder's mass is m = 10 kg.

    The cylinder's radius is r  = 15 cm (0.15 metres).

    μs = 0.25 is the static friction coefficient.

    Angle of inclination: θ=30ο

    For rolling without skidding in case of a cylinder to:

    μ13tanθ

    tanθ3μ=3×0.25

    θtan-1(0.75)=37°

    Therefore for an angle above 37, the cylinder will start to skid.

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