Final answer:
The kinetic energy of rotation of a rigid body about a new parallel axis, given the mass m, distance a from the centre of mass, angular velocity ω, and radius of gyration K, is 1/2 m(a²+K²)ω². Option D is correct.
Step-by-step explanation:
The kinetic energy of a rotating rigid body about a new parallel axis can be found using the parallel-axis theorem, which states that the moment of inertia I for a new axis parallel to the axis through the centre of mass is given by I = Icm + ma2, where Icm is the moment of inertia about the centre of mass, m is the mass of the body, and a is the distance between the new axis and the axis through the centre of mass.
The radius of gyration K is related to the moment of inertia via Icm = mK2. Thus, the rotational kinetic energy KErot about the new axis is given by KErot = 0.5 * (Icm + ma2)ω2 = 0.5 * (mK2 + ma2)ω2. Therefore, the correct option is d. 1/2 m(a2+K2)ω2.