A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period $2\;s$ at $T=0^{\circ}C$. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope $S$. If the coefficient of linear expansion of metal is $\alpha$ then the value of $S$ is :

Question

$\begin{array}{1 1}(1) \alpha \\ (2) \large\frac{\alpha}{2} \\ (3) 2 \alpha \\ (4) \large\frac{1}{\alpha} \end{array}$