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A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kₜ) as well as rotational kinetic energy (Kᵣ) simultaneously. The ratio Kᵣ : (Kₜ + Kᵣ) for the sphere is

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

Correct answer: 7 : 10

Solution

For a solid sphere in pure rolling motion, the rotational kinetic energy (Kᵣ) is (2/5)mv², and the translational kinetic energy (Kₜ) is (1/2)mv². The total kinetic energy is Kₜ + Kᵣ = (1/2)mv² + (2/5)mv² = (7/10)mv². Thus, the ratio Kᵣ : (Kₜ + Kᵣ) = (2/5) / (7/10) = 7:10.

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