A solid sphere of mass ' M ' and radius ' R ' is rotating about its diameter. A solid cylinder of same mass and radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation ( K _ sphere to K _ cylinder ) will be

Step-by-step solution

Kinetic energy of sphere is given by: aligned & E_ sphere = 1 2 I_ sphere _ sphere ^2 & E_ sphere = 1 2 2 5 m R^2 _ sphere ^2 aligned Kinetic energy of cylinder is given by: aligned & E_ cylinder = 1 2 I_ cylinder _ cylinder ^2 & E_ cylinder = 1 2 1 2 m R^2 _ cylinder ^2 & Given, _ cylinder =2 _ sphere & E_ sphere E_ cylinder = 1 5 aligned