When a liquid filled in two vessels A and B of equal volumes, is heated, the coefficients of apparent expansions of the liquids are found to be $\gamma_1\: and \: \gamma_2$ respectively. If $\alpha_1$ be the coefficient of linear expansion of A, then the coefficient of linear expansion of B will be :

Question

$\begin {array} {1 1} (1)\;\large\frac{\gamma_2-\gamma_1}{3}+\alpha_1 & \quad (2)\;\large\frac{\gamma_2-\gamma_1}{3}-\alpha_1 \\ (3)\;\large\frac{\gamma_1-\gamma_2}{3}+\alpha_1 & \quad (4)\;\large\frac{\gamma_1-\gamma_2}{3}-\alpha_1 \end {array}$