question_answer

A cylinder of radius R and mass M rolls without slipping down a plane inclined at an angle\[\theta \]. Coefficient of friction between the cylinder and the plane is p. For what maximum inclination 0 the cylinder rolls without slipping?

A) \[\theta ={{\tan }^{-1}}\left[ \frac{4}{3}\mu  \right]\]    

B) \[\theta ={{\tan }^{-1}}\left[ 2\mu  \right]\]

C)  \[\theta ={{\tan }^{-1}}\left[ 3\mu  \right]\]     

D)   \[\theta ={{\tan }^{-1}}\left[ \frac{3}{2}\mu  \right]\]