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A uniform rod is hinged at one end and oscillates in a vertical plane as a physical pendulum with a time period of 2 seconds. The rod has a coefficient of linear expansion alpha = 2 * 10⁻⁵ /degC. If the temperature increases by 10 degC (take g = pi² m/s²), which of the following statements is/are correct?

1. Its original length is 1.5 m
2. Its time period increases by 10⁻⁴ sec (approx.)
3. Its time period decreases by 2 * 10⁻⁴ sec (approx.)
4. Its original length is 3 m

Correct answer: Its original length is 1.5 m

Solution

From T = 2 s and g = pi²: L = 3g/(2*pi²) = 3*pi²/(2*pi²) = 1.5 m. Change in time period: delta Tₚ = T*(1/2)*alpha*delta_theta = 2*(0.5)*(2e-5)*(10) = 2e-4 s (increase).

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