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A simple pendulum made of a bob of mass \( m \) and a metallic wire of negligible mass has time period \( 2 \mathrm{~s} \)
\( \mathrm{P} \) at \( T=0^{\circ} \mathrm{C} \). If the temperature of the wire is increased

W 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
(a) \( \frac{1}{\alpha} \)
(b) \( 2 \alpha \)
(c) \( \alpha \)
(d) \( \frac{1}{\alpha} \)
(JEE Main)
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