Question

If a simple pendulum has point of suspension at rest, the period of oscillation $T$ is related to length of the pendulum $l$ as:

• A. $\frac{l}{T}=\text{constant}$
• B. $\frac{l^2}{T}=\text{constant}$
• C. $\frac{l}{T^2}=\text{constant}$
• D. $\frac{l^2}{T^2}=\text{constant}$

Answer 1

The correct option is C $\frac{l}{T^2}=\text{constant}$

Time period of simple pendulum is,
$T=2\pi \sqrt{\frac{l}{g}}$
Squaring both sides,
$\Rightarrow \frac{l}{T^2}=\frac{g}{4{\pi }^2}=\text{constant}$
Hence, option $\left(c\right)$ is correct.