question_answer

The coefficient of linear expansion of an inhomogeneous rod changes linearly from \[{{\alpha }_{1}}\] to \[{{\alpha }_{2}}\] from one end to other end of the rod. The effective coefficient of linear expansion of the rod is

A) \[({{\alpha }_{1}}+{{\alpha }_{2}})\]            

B) \[\frac{1}{2}({{\alpha }_{1}}+{{\alpha }_{2}})\]   

C) \[\sqrt{{{\alpha }_{1}}{{\alpha }_{2}}}\]              

D) \[({{\alpha }_{1}}-{{\alpha }_{2}})\]