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A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination 30 ^o(c)

Q7.31     A cylinder of mass 10kg  and radius 15cm  is rolling perfectly on a plane of inclination 30^{0}. The coefficient
              of static friction \mu _{s}=0.25.

             (c) If the inclination \Theta of the plane is increased, at what value of \Thetadoes the cylinder begin to skid, and not roll perfectly?

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In case of rolling without any skidding is given by :

                                             \mu\ =\ \frac{1}{3}\tan \Theta

Thus                                  \tan \Theta\ =\ 3 \mu

or                                                      =\ 3 \times (0.25)\ =\ 0.75

or                                              \Theta \ =\ 37.87 ^{\circ}

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