question_answer

Coefficient of linear expansion of brass and steel rods are \[{{\alpha }_{1}}\] and \[{{\alpha }_{2}}.\] Lengths of brass and steel rods are \[{{\ell }_{1}}\]and \[{{\ell }_{.2}}\] respectively. If \[({{\ell }_{2}}-{{\ell }_{1}})\]is maintained same at all temperatures, which one of the following relations holds good?                                                                                                                                                    

A)  \[{{\alpha }_{1}}{{\ell }_{2}}={{\alpha }_{2}}{{\ell }_{1}}\]                             

B)   \[{{\alpha }_{1}}\ell _{2}^{2}={{\alpha }_{2}}\ell _{1}^{2}\]

C)   \[\alpha _{1}^{2}{{\ell }_{2}}=\alpha _{2}^{2}{{\ell }_{1}}\]                        

D)   \[{{\alpha }_{1}}{{\ell }_{1}}={{\alpha }_{2}}{{\ell }_{2}}\]