A clock which keeps correct time at 20$℃$, is subjected to 40$℃$. If coefficient of linear expansion of the pendulum is $12 imes 10^{- 6}℃^{- 1}$. How much will it gain or lose time?

Question

A clock which keeps correct time at 20$℃$, is subjected to 40$℃$. If coefficient of linear expansion of the pendulum is $12 	imes 10^{- 6}℃^{- 1}$. How much will it gain or lose time?

Dr. Abubacker · Accepted Answer

(a) Time period, $T = 2\pi\sqrt{\frac{1}{g}}$
$\frac{\mathrm{\Delta}T}{T} = \frac{1}{2}\ \frac{\mathrm{\Delta}l}{l} = \frac{1}{2}\alpha\mathrm{\Delta}	heta$
=$\frac{1}{2} 	imes 12 	imes 10^{- 6}(40 - 20) = 12 	imes 10^{- 5}$
$\mathrm{\Delta}T = T 	imes 12 	imes 10^{- 5}$
= $24 	imes 60 	imes 60 	imes 12 	imes 10^{- 5}$
= 10.3 s ${day}^{- 1}$

Q. A clock which keeps correct time at 20$℃$, is subjected to 40$℃$. If coefficient of linear expansion of the pendulum is $12 \times 10^{- 6}℃^{- 1}$. How much will it gain or lose time?

Explanation

Reviewed by Dr. Abubacker

Want more practice?