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  4. The graph between the time period and the length of a simple pendulum is

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Q. The graph between the time period and the length of a simple pendulum is

MHT CETMHT CET 2008

Solution:

The time period of a simple pendulum is
image
$T=2 \pi \sqrt{\frac{l}{g}}$
Here, $l$ is the length of the pendulum. On squaring both sides
$T^{2}=\frac{4 \pi^{2} l}{g}$
$\Rightarrow T^{2} \propto l$
So, the graph between time period $T$ and length $l$ of the pendulum is a parabola.