Using a simple pendulum experiment $g$ is determind by measuring its time period $T$. Which of the f

Question

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

Professor PC Thomas Classes · Answer

The time period of a simple pendulum is given by $T = 2\pi\sqrt{\frac{L}{g}}$. Squaring both sides yields $T^2 = \frac{4\pi^2}{g} L$. This shows that $L$ is directly proportional to $T^2$. Therefore, the graph of $L$ versus $T$ is a parabola opening towards the length ($L$) axis, and the graph of $L$ versus $T^2$ is a straight line passing through the origin.