Correct choice is (c) 0.5 I.ω^2
Explanation: When a body of mass moment of inertia I (about a given axis) is rotated about that axis, with an angular velocity ω, then it possesses some kinetic energy. In this case,
Kinetic energy of rotation = 1/ 2I.ω^2
When a body has both linear and angular motions e.g. in the locomotive driving wheels and wheels of a moving car, then the total kinetic energy of the body is equal to the sum of kinetic energies of translation and rotation.
∴ Total kinetic energy = 1/ 2mv^2 +1/ 2I.ω^2