A sphere of mass 2 kg and radius 5 cm rolls without slipping along a horizontal plane. The velocity of its centre of mass is 10 cm/s. The kinetic energy of the sphere is:
Correct answer: B. 0.014 J
- A. 0.07 J
- B. 0.014 J
- C. 0.025 J
- D. 1.25 J
Explanation
The correct option is B. When calculating the kinetic energy of a rolling object, both the translational and rotational kinetic energy components should be considered. In this case, the correct calculation yields 0.014 J. Options A, C, and D are incorrect because they do not consider the rotational kinetic energy component or have incorrect calculations.T = ½ I ω² + ½ m v²I = (2/5) m r² and v = ωr as it is rolling without slipping.∴ I = (7/10) m v² = (7/10) × 2 × 0.1² = 0.014 J
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