A) 18 cm
B) 4.5 cm
C) 2.25 cm
D) 9 cm
Correct Answer: D
Solution :
Here: The coefficient of volumetric expansion \[\gamma =18\times {{10}^{-5}}/{}^\circ C\] Initial volume \[V={{10}^{-6}}{{m}^{3}}\] Area of cross section A \[=0.002c{{m}^{2}}=2\times {{10}^{-7}}{{m}^{2}}\] Initial temperature \[{{T}_{1}}=0{}^\circ C\] Final temperature \[{{T}_{2}}=100{}^\circ C\] The final volume is \[V=V[1+({{T}_{2}}-{{T}_{2}})]\] \[={{10}^{-6}}[1+18\times {{10}^{-5}}(100-0)]\] and \[V=1.018\times {{10}^{-6}}\] Change in volume is \[\Delta V=A\times \Delta l=V-V\] or \[=2\times {{10}^{-7}}\times \Delta l\] \[=1.018\times {{10}^{-6}}-{{10}^{6}}\] \[2\times {{10}^{-7}}\times \Delta l=0.018\times {{10}^{-6}}\] Hence,\[\Delta l=\frac{0.018\times {{10}^{-6}}}{2\times {{10}^{-7}}}=0.09\,m=9\,cm\]
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