A pendulum clock loses 12 s a day if the tem | vedclass

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(A) The time lost or gained by a pendulum clock due to temperature change is given by $\Delta t = \frac{1}{2} \alpha (\Delta 	heta) T$,where $\alpha$

Vedclass · Accepted Answer

$25$

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(A) The time lost or gained by a pendulum clock due to temperature change is given by $\Delta t = \frac{1}{2} \alpha (\Delta 	heta) T$,where $\alpha$ is the coefficient of linear expansion,$\Delta 	heta$ is the change in temperature,and $T$ is the time period.Let $	heta$ be the temperature at which the clock shows the correct time.At $40^{\circ} C$,the clock loses $12 \ s$: $12 = \frac{1}{2} \alpha (40 - 	heta) T$ ... $(i)$At $20^{\circ} C$,the clock gains $4 \ s$: $4 = \frac{1}{2} \alpha (	heta - 20) T$ ... $(ii)$Dividing equation $(i)$ by $(ii)$:$\frac{12}{4} = \frac{40 - 	heta}{	heta - 20}$$3 = \frac{40 - 	heta}{	heta - 20}$$3(	heta - 20) = 40 - 	heta$$3	heta - 60 = 40 - 	heta$$4	heta = 100$$	heta = 25^{\circ} C$

$A$ pendulum clock loses $12 \ s$ a day if the temperature is $40^{\circ} C$ and gains $4 \ s$ a day if the temperature is $20^{\circ} C$. The temperature at which the clock will show the correct time is: (in $^{\circ} C$)

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