A) 18 cm
B) 4.5 cm
C) 2.25 cm
D) 9 cm
Correct Answer: D
Solution :
The coefficient of volumetric expansion \[\gamma =18\times {{10}^{-5}}\,{}^\circ C\] \[V={{10}^{-6}}{{m}^{3}}\] Area of cross-section A \[0.002\times c{{m}^{2}}=2\times {{10}^{-7}}{{m}^{2}}\] Initial temperature\[={{T}_{1}}=0{}^\circ C\] Final temperature \[={{T}_{2}}=100{}^\circ C\] The final volume is \[V=V\,[1+\gamma \,({{t}_{2}}-{{t}_{1}})]\] \[={{10}^{-6}}[1+18\times {{10}^{-5}}(100-10)]\] \[V=1.018\times {{10}^{-6}}\] Change in volume is \[\Delta V=A\times \Delta I=V-V\] \[=2\times {{10}^{-7}}\times \Delta I\] \[=1.018\times {{10}^{-6}}-{{10}^{6}}\] \[2\times {{10}^{7}}\times \Delta I=0.018\times {{10}^{-6}}\] \[\Delta I=9\,cm\]
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