A) \[{{10}^{2}}\]
B) \[{{10}^{-2}}\]
C) \[{{10}^{-3}}\]
D) \[{{10}^{-4}}\]
Correct Answer: D
Solution :
Initial temperature\[{{T}_{1}}={{0}^{o}}C\] Initial density\[{{\rho }_{1}}=10\,\,g/\sec \] Final temperature\[{{T}_{2}}={{100}^{o}}C\] Final density\[{{\rho }_{2}}=9.7\,\,g/cc\] coefficient of volumetric expression \[{{\alpha }_{v}}=\frac{\Delta \rho }{{{\rho }_{1}}\times \Delta T}=\frac{{{\rho }_{1}}-{{\rho }_{2}}}{\rho ({{T}_{1}}-{{T}_{2}})}\] \[=\frac{10-9.7}{10(100-0)}=\frac{0.3}{1000}=3\times {{10}^{-4}}\] Hence, coefficient of linear expansion is \[{{\alpha }_{l}}=\frac{{{\alpha }_{v}}}{3}=\frac{3\times {{10}^{-4}}}{3}={{10}^{-4}}{{/}^{o}}C\]
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