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Question

# 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
3 : 1
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B
2 : 3
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C
1 : 5
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D
1 : 4
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Solution

## The correct option is C 1 : 5Kinetic energy of sphere is given by Esphere=12Isphereω2sphere Esphere=12×25mR2×ω2sphere Kinetic energy of cylinder is given by Ecylinder=12Icylinderω2cylinder Ecylinder=12×12mR2×ω2cylinder Given, ωcylinder=2ωsphere ∴EsphereEcylinder=15

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