Properties Of Solids And Liquids Question 540
Question: A pendulum clock keeps correct time at $ 0{}^\circ C $ . Its mean coefficient of linear expansions is a$ {{\alpha }^{o}}{{C}^{-1}} $ . The loss in seconds per day by the clock if the temperature rises by $ t{}^\circ C $ is
Options:
A) $ \frac{\frac{1}{2}\alpha t\times 864000}{1-\frac{\alpha t}{2}} $
B) $ \frac{1}{2}\alpha t\times 86400 $
C) $ \frac{\frac{1}{2}\alpha t\times 86400}{{{( 1+\frac{\alpha t}{2} )}^{2}}} $
D) $ \frac{\frac{1}{2}\alpha t\times 86400}{1+\frac{\alpha t}{2}} $
Show Answer
Answer:
Correct Answer: B
Solution:
T = Time period
$ T\propto {{\ell }^{1/2}} $
$ \frac{\Delta T}{T}=\frac{1}{2}\frac{\Delta \ell }{\ell }=\frac{1}{2}\alpha t; $
$ \Delta T=\frac{1}{2}\alpha tT=\alpha t $
Total loss $ =\frac{1}{2}\alpha t\times 86400 $
