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 1: 3 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: E_ sphere = 1 2 I_ sphere _ sphere ^2E_ sphere = 1 2 2 5 m R^2 _ sphere ^2 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