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A pendulum clock loses 12 s a day if the temperature is 40°C and gains 4 s a day if the temperature is 20°C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion (α) of the metal of pendulum shaft are respectively:

1. 25°C; α = 1.85 × 10⁻⁵/°C
2. 60°C; α = 1.85 × 10⁻⁴/°C
3. 30°C; α = 1.85 × 10⁻³/°C
4. 55°C; α = 1.85 × 10⁻²/°C

Correct answer: 25°C; α = 1.85 × 10⁻⁵/°C

Solution

The clock shows correct time at a temperature where the effects of thermal expansion balance out the timekeeping errors caused by temperature changes. The calculations indicate that at 25°C, the pendulum's length adjusts appropriately to maintain accurate time, and the derived coefficient of linear expansion reflects the material's response to temperature variations.

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