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A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be

1. R² / (K² + R²)
2. (K² + R²) / R²
3. K² / R²
4. K² / (K² + R²)

Correct answer: K² / (K² + R²)

Solution

The total energy of the rolling ball is the sum of its translational and rotational kinetic energies. The rotational energy fraction is given by the ratio of rotational kinetic energy to total energy, which simplifies to K² / (K² + R²) using the moment of inertia I = mK².

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