A pendulum clock loses 12 s a day if the temperature is 40⁰ C and gains 4s a day if the temperature is 20⁰C. The temperature at which the clock will show correct time, and the co – efficient of linear expansion (a) of the metal of the pendulum shaft are respectively

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Solution

The correct option is D

$\frac{1}{2} α (40 - T) \times 86400 = 12 s . . . . (1) \frac{1}{2} α (T - 20) \times 86400 = 4 . . . . (2)$
On dividing (1) by (2) and solving

$T = 25^{\circ} C$

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A pendulum clock loses 12 seconds a day if the temperature is $40^{\circ} C$ and goes fast by 4 seconds a day if the temperature is $20^{\circ} C$ . Find the temperature at which the clock will show correct time, and the coefficient of linear expansion of the metal of the pendulum shaft.