A) \[2.25\times {{10}^{-6}}s~\]
B) \[2.5\times {{10}^{-7}}s\]
C) \[5\times {{10}^{-7}}s~\]
D) \[1.125\times {{10}^{-6}}s\]
Correct Answer: A
Solution :
Time period of oscillation, \[T=2\pi \sqrt{\frac{l}{g}}\] \[\Rightarrow \] \[\frac{dT}{T}=\frac{1}{2}\frac{dl}{l}\] As, \[\frac{dl}{l}=\alpha dt\] \[\Rightarrow \] \[\frac{dT}{T}=\frac{1}{2}\alpha dt\] \[=\frac{1}{2}\times 9\times {{10}^{-7}}\times (30-20)\] \[=4.5\times {{10}^{-6}}\] \[\therefore \]Loss in time \[=4.5\times {{10}^{-6}}\times 0.5\] \[=2.25\times {{10}^{-6}}s\]
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