A) \[11\times {{10}^{-6}}\] cm longer
B) \[11\times {{10}^{-6}}\]cm shorter
C) \[11\times {{10}^{-5}}\] cm shorter
D) \[11\times {{10}^{-5}}\] cm longer
Correct Answer: C
Solution :
[c] \[L={{L}_{0}}\left( 1+\alpha \,\Delta \theta \right)\Rightarrow \frac{{{L}_{1}}}{{{L}_{2}}}=\frac{1+\alpha {{\left( \Delta \theta \right)}_{1}}}{1+\alpha {{\left( \Delta \theta \right)}_{2}}}\] \[\Rightarrow \frac{10}{{{L}_{2}}}=\frac{1+11\times {{10}^{-6}}\times 20}{1+11\times {{10}^{-6}}\times 19}\Rightarrow {{L}_{2}}=9.99989\] \[\Rightarrow \]Length is shorten by \[10-9.99989=0.00011=11\times {{10}^{-5}}\,cm.\]
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