A) \[{{10}^{-4}}\]
B) \[3\times {{10}^{-4}}\]
C) \[19.7\times {{10}^{-3}}\]
D) \[{{10}^{-3}}\]
Correct Answer: A
Solution :
Given : Density of substance at \[0{{\,}^{o}}C\]is\[{{\rho }_{o}}=10g/cc\] Density of substance at \[100{{\,}^{o}}C\]is \[{{\rho }_{100}}=9.7g/cc\] From the relation, \[{{\rho }_{t}}=\frac{{{\rho }_{o}}}{1+\gamma t}={{\rho }_{o}}(1-\gamma t)\] \[9.7=10[1-\gamma \times (100-0)]\Rightarrow 1-100\gamma \] \[=0.97\Rightarrow \gamma =\frac{0.03}{100}=3\times {{10}^{-4}}/{{\,}^{o}}C\] Therefore, linear coefficient of expansion \[\alpha =\frac{\gamma }{3}\] So, \[\alpha =\frac{3\times {{10}^{-4}}/{{\,}^{o}}C}{3}=1\times {{10}^{-4}}/{{\,}^{o}}C\]
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