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A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (Eₛₚₕₑᵣₑ/E_cylinder) will be

Asked in NEET-II 2016 · Rotational energy and released bodies

• (1) 2 : 3
• (2) 1 : 5
• (3) 1 : 4
• (4) 3 : 1

Step-by-step solution

Why the other options are wrong

• (1) comes from out of reach: the two moments of inertia are in the ratio (2/5)/(1/2)=4/5 and the ω² factor is exactly 4, so the energy ratio can only be 4/5×1/4=1/5, or 4/5×4=(16)/5 if the factor is applied to the wrong body
• (3) comes from using the ω² factor of 4 on its own and treating the two moments of inertia as equal
• (4) comes from the cylinder has both the larger moment of inertia and twice the angular speed, so its rotational energy must be the larger of the two; any ratio above 1 is out

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