A) \[{{55}^{o}}C;\alpha =1.85\times {{10}^{-2}}{{/}^{o}}C\]
B) \[{{25}^{o}}C;\alpha =1.85\times {{10}^{-5}}{{/}^{o}}C\]
C) \[{{60}^{o}}C;\alpha =1.85\times {{10}^{-4}}{{/}^{o}}C\]
D) \[{{30}^{o}}C;\alpha =1.85\times {{10}^{-3}}{{/}^{o}}C\]
Correct Answer: B
Solution :
\[T=2\pi \sqrt{\frac{\ell }{g}}\] \[\frac{\Delta T}{T}=\frac{1}{2}\frac{\Delta \ell }{\ell }\]When clock gain 12 sec \[\frac{12}{T}=\frac{1}{2}\alpha (40-\theta )\] ...(1) When clock lose 4 sec. \[\frac{4}{T}=\frac{1}{2}\alpha (\theta -20)\] ...(2) From equation (1) & (2) \[3=\frac{40-\theta }{\theta -20}\] \[3\theta =60=40-\theta \] \[4\theta =100\] \[\]from equation (1) \[\frac{12}{T}=\frac{1}{2}\alpha (40-25)\] \[\frac{12}{24\times 3600}=\frac{1}{2}\alpha \times 15\] \[\alpha =\frac{24}{24\times 3600\times 15}\]\[\]
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