Question Detail

The rotational kinetic energy is (1/2)Iω². For a disc, I = (1/2)MR². If it's rolling, v = Rω, so K_rot = (1/2)(1/2 MR²)(v²/R²) = (1/4)Mv². That would be 1/4 mv². But the question just says 'rotational kinetic energy of disc' without specifying if it's rolling or just spinning. If it's spinning with some ω, then K_rot = (1/2)Iω², and if we express it in terms of v (which is not defined), it's ambiguous. Option B is 1/2 mv², which is translational KE. For a disc that is only rotating (not translating), if v is the speed of a point on the rim, then v=ωR, and K_rot = (1/2)(1/2 mR²)(v²/R²) = 1/4 mv². So the correct should be 1/4 mv², which is not B. Option A is 1/4 mv². So likely A is correct.