Rotational Kinetic Energy, Work & Power question from MHT CET 2024 (4 May, Shift 1)

Answer: (b)

1. Cylinder: $K_c = \frac{1}{2}\left(\frac{1}{2}MR^2\right)\omega^2 = \frac{MR^2\omega^2}{4}$
2. Sphere at $\frac{\omega}{2}$: $K_s = \frac{1}{2}\left(\frac{2}{5}MR^2\right)\frac{\omega^2}{4} = \frac{MR^2\omega^2}{20}$
3. $\frac{K_s}{K_c} = \frac{1}{5}$
4. So the answer is (b) $1 : 5$.