A solid sphere of mass ' m ' and radius ' R ' is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with angular speed twice that of sphere. The ratio of kinetic energy of sphere to kinetic energy of cylinder will be

Step-by-step solution

Given a solid sphere and solid cylinder with equal mass m and radius R , rotating about their respective axes with angular speeds _c = 2 _s . The moment of inertia for a solid sphere is I_s = 2 5 mR^2 , yielding rotational kinetic energy KE_s = 1 2 I_s _s^2 = 1 5 mR^2 _s^2 . For the solid cylinder, I_c = 1 2 mR^2 , and with _c = 2 _s , its kinetic energy becomes KE_c = 1 2 I_c _c^2 = mR^2 _s^2 . The ratio is therefore KE_s KE_c = 1 5 mR^2 _s^2 mR^2 _s^2 = 1 5 . Answer: B