Chapter 11, Problem 29P

To determine

To Find: The length of the simple pendulum.

Answer to Problem 29P

The length of a simple pendulum is $0.99\text{ m}$ .

Explanation of Solution

Given info:

Period $T=2\text{ s}$

Formula used:

The expression for period.

  $T=2\pi \times \sqrt{\frac{l}{g}}$

Here,

  $T$ is time period of pendulum,

  $l$ is the length of pendulum,

  $g$ is the acceleration due to gravity.

Calculation:

The above expression can be written as:

  $\begin{array}{l}T=2\pi \times \sqrt{\frac{l}{g}}\\ l=\frac{T^2\times g}{4\times {\pi }^2}\end{array}$

Substitute the given values to the value of length

  $l=\frac{T^2\times g}{4\times {\pi }^2}=\frac{2^2\times 9.8}{4\times {\pi }^2}=0.99\text{ m}$

Conclusion:

Thus, the length of a simple pendulum when it makes exactly one swing per second is $0.99\text{ m}$ .