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 (Esphere/Ecylinder) will be
Kinetic energy of sphere is given by
Esphere=12Isphereω2sphere
Esphere=12×25mR2×ω2sphere
Kinetic energy of cylinder is given by
Ecylinder=12Icylinderω2cylinder
Ecylinder=12×12mR2×ω2cylinder
Given, ωcylinder=2ωsphere
∴EsphereEcylinder=15