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A spherical ball rolls on a table without slipping. Then the fraction of its total energy associated with rotation is

1. 2/5
2. 2/7
3. 3/5
4. 3/7

Correct answer: 3/7

Solution

For a rolling sphere without slipping, the total energy is the sum of translational and rotational kinetic energy. The rotational energy fraction is given by I/(I + mR²), where I = (2/5)mR² for a sphere. Simplifying, the fraction becomes 2/7.

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