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 $



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