Using a simple pendulum experiment g is determined by measuring its time period T. Which of the following plots represen

Question

Using a simple pendulum experiment g is determined by measuring its time period T. Which of the following plots represent the correct relation between the pendulum length L and time period T?

Accepted Answer

Given: For a simple pendulum, the time period is related to length by

T = 2\pi\sqrt{\frac{L}{g}}

Find: Which plot correctly represents the relation between $L$ and $\dfrac{1}{T^2}$ .

Squaring both sides,

T^2 = \frac{4\pi^2 L}{g}

Taking reciprocal,

\frac{1}{T^2} = \frac{g}{4\pi^2} \cdot \frac{1}{L}

So,

\frac{1}{T^2} \propto \frac{1}{L}

Hence $\dfrac{1}{T^2}$ varies inversely with $L$ , so the graph must be a decreasing rectangular hyperbola. Therefore, the correct option is D.

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