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The angular velocity and the amplitude of a simple pendulum is ω and a respectively. At a displacement x from the mean position if its kinetic energy is T and potential energy is V, then the ratio of T to V is

1. (a² - x²)ω² / x²ω²
2. x²ω² / (a² - x²ω²)
3. x² / (a² - x²)
4. (a² - x²) / x²

Correct answer: (a² - x²)ω² / x²ω²

Solution

The kinetic energy (T) of the pendulum is proportional to (a² - x²)ω², and the potential energy (V) is proportional to x²ω². Thus, the ratio T/V becomes (a² - x²)ω² / x²ω².

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