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 :
