A solid cylinder is rolling down on an inclined plane of angle . The coefficient of static friction between the plane and the cylinder is _s . The condition for the cylinder not to slip is

Step-by-step solution

Linear acceleration for rolling, a= g 1+k^2 / R^2 For cylinder, k^2 R^2 = 1 2 a_ cylinder = 2 3 g For rotation, the torque F R=I (M R^2 ) / 2 (where, F= force of friction) But R =a F= M 2 aF= M 2 2 3 g = M 3 g _s= F N , where N is normal reaction, _s= M 3 g M g = 3 For rolling without slipping of a roller down, the inclined plane, 3 _s .