Rotational Kinetic Energy, Work & Power question from MHT CET 2025 (22 Apr, Shift 1)

Answer: (b)

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