A solid cylinder and a solid sphere having the same mass and radius roll down on the same smooth inclined plane. The ratio of the acceleration of the cylinder (a_c) to that of the sphere (a_s) is

Step-by-step solution

The acceleration of a body rolling down an inclined plane is given by a = g 1 + I MR^2 . For a solid cylinder, I_c = 1 2 MR^2 . a_c = g 1 + 1 2 = 2 3 g For a solid sphere, I_s = 2 5 MR^2 . a_s = g 1 + 2 5 = 5 7 g The ratio of the acceleration of the cylinder to that of the sphere is: a_c a_s = 2 3 g 5 7 g = 14 15 Answer: 14 15