Properties Of Solids And Liquids Question 603
Question: A pendulum clock keeps correct time at $ 0{}^\circ C $ . Its mean coefficient of linear expansions is $ \alpha /{}^\circ C $ , then 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}} $
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Answer:
Correct Answer: B
Solution:
Loss in time per second $ \frac{\Delta T}{T}=\frac{1}{2}a\Delta \theta =\frac{1}{2}\alpha (t-0) $
$ \Rightarrow $ loss in time per day $ \Delta t=( \frac{1}{2}\alpha t )t=\frac{1}{2}\alpha t\times (24\times 60\times 60)=\frac{1}{2}\alpha t\times 86400 $
