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At maximum compression, the solid cylinder will stop so loss in kinetic energy of the cylinder equals gain in potential energy of the spring. What is the expression for the energy?

1. 1/2 mv² + 1/2 Iω² = 1/2 kx²
2. 1/2 mv² + 1/2 mR² (v²/R²) = 1/2 kx²
3. 1/2 mv² + 1/2 mR² (v²/R²) = kx²
4. 1/2 mv² + 1/2 Iω² = kx²

Correct answer: 1/2 mv² + 1/2 Iω² = 1/2 kx²

Solution

At maximum compression, the total mechanical energy is conserved. The initial kinetic energy of the cylinder, which includes both translational (1/2 mv²) and rotational (1/2 Iω²) components, is converted into the potential energy of the spring (1/2 kx²).

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