A) \[80.0096\,\,cm\]
B) \[80.0272\,\,cm\]
C) \[1\,\,cm\]
D) \[25.2\,\,cm\]
Correct Answer: A
Solution :
Key Idea: Coefficient of linear expansion \[=\frac{change\text{ }in\text{ }length}{initial\text{ }length\times temperature\text{ }difference}\] Let \[{{l}_{1}}\] and \[{{l}_{0}}\] be the length at \[{{t}^{\circ }}C\] and \[{{0}^{\circ }}C\] then at temperature \[t\] \[a=\frac{{{l}_{1}}-{{l}_{0}}}{{{l}_{0}}\,t}\] \[\Rightarrow \] \[{{l}_{t}}={{l}_{0}}\left( 1+a\,t \right)\] Where \[a\] is linear coefficient of expansion \[\therefore \] \[{{l}_{t}}=1\left[ 1+11\times {{10}^{-6}}\times \left( {{40}^{\circ }}-{{20}^{\circ }} \right) \right]\] \[{{l}_{t}}=1.00022\] cm Length of copper rod at \[40{{\,}^{\circ }}C\] is \[l_{t}^{'}=l_{0}^{'}\left( 1+a'\,t \right)\] \[=80\left[ 1+17\times {{10}^{-6}}\left( {{40}^{\circ }}-{{20}^{\circ }} \right) \right]\] \[l_{t}^{'}=80.0272\,cm\] Number of cms observed on the scale is \[=\frac{80.0272}{1.00022}=80.0096\]
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