In the following table, the relation of the graph in column-$I$ and the shape of the graph in column-$II$ is shown. Match them appropriately.
Column-$I$Column-$II$
$(a)$ $T^2 \to l$$(i)$ Linear
$(b)$ $T^2 \to g$$(ii)$ Parabolic
$(c)$ $T \to l$$(iii)$ Hyperbolic

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(A) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{l}{g}}$.
$(a)$ For $T^2 \to l$: Squaring both sides, $T^2 = \frac{4\pi^2}{g} l$. Since $T^2 \propto l$, the graph is a straight line passing through the origin. Thus, $(a-i)$.
$(b)$ For $T^2 \to g$: From $T^2 = \frac{4\pi^2 l}{g}$, we have $T^2 \propto \frac{1}{g}$. This represents a rectangular hyperbola. Thus, $(b-iii)$.
$(c)$ For $T \to l$: From $T = 2\pi \sqrt{\frac{l}{g}}$, we have $T \propto \sqrt{l}$. This represents a parabolic curve. Thus, $(c-ii)$.
Therefore, the correct matching is $(a-i, b-iii, c-ii)$.

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