STANDARDPhysics-Rotational Motion
STANDARD Physics Kinetic Energy of Rotation MCQ Question
Type: MCQ-conceptual-Medium
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/Ecylinder) will be
A
2 : 3
B
1 : 5
C
1 : 4
D
3 : 1
Correct Answer
Option B
Detailed Explanation
The kinetic energy of rotation for a sphere is (1/2)Iₛₚₕₑᵣₑωₛₚₕₑᵣₑ² and for a cylinder is (1/2)Icyₗᵢₙdₑᵣωcyₗᵢₙdₑᵣ². Given ωcyₗᵢₙdₑᵣ = 2ωₛₚₕₑᵣₑ, substituting the moments of inertia and simplifying gives the ratio 1:5.
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