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 an angular speed twice that of the sphere . The ratio of their kinetic energies of rotation (E_("sphere") // E_("cylinder")) will be

A solid sphere of mass m and radius R is rotating about its diameter A

1.	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 an angular speed twice that of the sphere . The ratio of their kinetic energies of rotation (E_("sphere") // E_("cylinder")) will be
Answer» `2 : 3` `1 : 5` `1 : 4` `3 : 1` Solution :`(E_("Sphere"))/(E_("CYLINDER")) = ((1)/(2) I_(s) omega_(s)^(2))/((1)/(2) I_(C) omega_(c)^(2)) = (I_(s) omega_(s)^(2))/(I_(c) omega_(c)^(2))` Here , `I_(s) = (2)/(5) m R^(2) , I_(c) = (1)/(2) mR^(2) , omega_(c) = 2 omega_(s)` `(E_("Sphere"))/(E_("Cylinder")) = ((2)/(5) mR^(2) xx omega_(s)^(2))/((1)/(2) mR^(2) xx (2 omega_(s))^(2)) = (4)/(5) xx (1)/(4) = (1)/(5)`