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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 energy of rotation (EsphereEcylinder) will be

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

The correct option is B 1 : 5EsphereEcylinder= 12Isωs212Icωc2=Isωs2Icωc2 Here, Is=25mR2, Ic=12mR2 ωc=2ωs EsphereEcylinder=25mR2×ωS212mR2×(2ωS)2=45×14=15

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