A composite bar of length $\;(l_{1} + l_{2})\;$ is made from two bars of length $\;l_{1}\;$ and $\;l_{2}\;$ . Their coefficients of linear expansion $\;\alpha_{1}\;$ and $\;\alpha_{2}\;$ respectively . The effective linear coefficient of composite bar

Question

$(a)\;\large\frac{l_{1} \alpha_{1} - l_{2} \alpha_{2}}{l_{1}-l_{2}}\qquad(b)\;\large\frac{l_{1} \alpha_{1} + l_{2} \alpha_{2}}{l_{1}+l_{2}}\qquad(c)\;\alpha_{1}+\alpha_{2}\qquad(d)\;\large\frac{\alpha_{1} + \alpha_{2}}{2}$