A clock which keeps correct time at $20^{\circ} \mathrm{C}$, is subjected to $40^{\circ} \mathrm{C}$. If coefficient of linear expansion of the pendulum is $12 imes 10^{-6} /{ }^{\circ} \mathrm{C}$. How much will it gain or lose time?

Question

A clock which keeps correct time at $20^{\circ} \mathrm{C}$, is subjected to $40^{\circ} \mathrm{C}$. If coefficient of linear expansion of the pendulum is $12 	imes 10^{-6} /{ }^{\circ} \mathrm{C}$. How much will it gain or lose time?

Aicharya · Accepted Answer

$T=2 \pi \sqrt{\frac{I}{g}}$ $\begin{aligned} \frac{\Delta T}{T} & =\frac{1}{2} \frac{\Delta l}{l}=\frac{1}{2} \alpha \Delta 	heta \ & =\frac{1}{2} 	imes 62 	imes 10^{-6}(40-20)=12 	imes 10^{-5} \ \Delta T & =T 	imes 12 	imes 10^{-5} \ & =24 	imes 60 	imes 60 	imes 12 	imes 10^{-5} \ & =10.3 \mathrm{~s} / 	ext { day }\end{aligned}$

A clock which keeps correct time at $20^{\circ} \mathrm{C}$, is subjected to $40^{\circ} \mathrm{C}$. If…

Solution