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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

Asked in CBSE AIPMT 2003 · Rolling kinematics and energy

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

Step-by-step solution

Why the other options are wrong

• (1) comes from this is greater than 1 for every K, so it cannot be a fraction of the total energy
• (2) comes from this is (Kᵣ)/(Kₜ), the rotational energy compared with the translational energy, not with the total
• (4) comes from this is the translational fraction, the complement of the answer; the two add to 1

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