A simple pendulum of length $L=1\text{ m}$ has a time period of approximately how many seconds? (Take $g={\pi }^2{\text{ m/s}}^2$)

Solution

1. The time period $T$ of a simple pendulum is given by the formula $T=2\pi \sqrt{\frac{L}{g}}$.
2. Substitute the given values $L=1\text{ m}$ and $g={\pi }^2{\text{ m/s}}^2$ into the equation.
3. Simplify the expression: $$\begin{array}{rl}T& =2\pi \sqrt{\frac{1}{{\pi }^2}}\\ & =2\pi \times \frac{1}{\pi }\\ & =2\text{ s}\end{array}$$.
4. Hence the answer is (B).