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Using the principle of conservation of mechanical energy, determine the speed of the object when it reaches the base of the inclined plane.

1. 3√2/4g
2. 1/2 Iω² + 1/2 mv² = mg × 3√2/4g
3. 1/2 Iω² = 3/4 mv² - 1/2 mv²
4. 1/2 (v²/R²) = mv² or I = 1/2 mR²

Correct answer: 1/2 Iω² + 1/2 mv² = mg × 3√2/4g

Solution

Option B represents the correct application of the law of conservation of mechanical energy, where the total energy (potential + kinetic) is conserved. The equation equates the initial potential energy to the sum of rotational and translational kinetic energies at the bottom of the incline.

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