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If a sphere is rolling, the ratio of the translational energy to total kinetic energy is given by

1. 7 : 10
2. 2 : 5
3. 10 : 7
4. 5 : 7

Correct answer: 5 : 7

Solution

For a rolling sphere, the total kinetic energy is the sum of translational and rotational kinetic energy. The translational energy is (1/2)mv², and the rotational energy is (1/2)Iω². Using the moment of inertia for a sphere, I = (2/5)mr², and the rolling condition v = rω, the ratio of translational energy to total kinetic energy is 5:7.

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