A) \[{{\alpha }_{1}}+{{\alpha }_{2}}\]
B) \[2{{\alpha }_{1}}+{{\alpha }_{2}}\]
C) \[{{\alpha }_{1}}\text{ }+\text{ }2{{\alpha }_{2}}\]
D) none of these
Correct Answer: C
Solution :
\[V={{V}_{0}}\left( 1+\gamma \theta \right)\] \[{{L}^{3}}={{L}_{0}}(1+{{\alpha }_{1}}\Delta \theta ){{L}^{2}}_{0}{{(1+{{\alpha }_{2}}\Delta \theta )}^{2}}\] \[1+\gamma \Delta \theta =\left( 1+{{\alpha }_{1}}\Delta \theta \right)\,{{\left( 1+{{\alpha }_{2}}\Delta \theta \right)}^{2}}\] \[\left[ \because \,\,\,{{L}^{3}}\,\,=\,\,{{L}^{3}}_{0}{{(1+\gamma \Delta \theta )}^{2}} \right]\] \[\therefore \,\,\,\gamma \,=\,{{\alpha }_{1}}+2{{\alpha }_{2}}\]
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