An inclined plane makes an angle 30^ with the horizontal. A solid sphere rolling down an inclined plane from rest without slipping has linear acceleration ( g= acceleration due gravity) ( 30^ =0.5 )

Step-by-step solution

Finding the linear acceleration of a solid sphere rolling without slipping requires applying Newton’s second law to both translational and rotational motion. The gravitational force component along the incline is Mg , while friction f_s acts up the incline. The net force equation along the incline is: Mg - f_s = Ma For rotation about the center, the torque from friction gives: f_s R = I The no-slip condition relates linear and angular acceleration: a = R . For a solid sphere, I = 2 5 MR^2 . Substituting yields: f_s