A solid sphere ( A ) of mass 5m and a spherical shell ( B ) of mass m , both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of A and B , they start rolling without slipping with an acceleration of a_A and a_B , respectively. The ratio of a_A and a_B is __________.

Step-by-step solution

For a body of mass M and radius R rolling without slipping under a force F applied tangentially at the highest point, the torque about the point of contact with the ground is = F(2R) . The moment of inertia about the point of contact is I = I_ cm + MR^2 . Using = I and the rolling without slipping condition a = R , we get: F(2R) = (I_ cm + MR^2) a R a = 2FR^2 I_ cm + MR^2 For the solid sphere A of mass 5m : I_ cm,A = 2 5 (5m)R^2 = 2mR^2 a_A = 2FR^2 2mR^2 + 5mR^2 = 2F 7m For the spherical shell B of mass m : I_ cm,B