Chapter 4, Problem 59SGA

To determine

Find the length of the pendulum.

Answer to Problem 59SGA

  $l=0.64meters$ .

Explanation of Solution

Given information:

  $T=2\pi \sqrt{\frac{l}{g}}$ , $T$ is $1.6\sec onds$ the time period, $l$ is length, $g$ is $9.8meters/\sec ondsquared$

acceleration due to gravity of oscillating pendulum.

Calculation:

Consider the given value and put in to the formula,

  $T=2\pi \sqrt{\frac{l}{g}}$

  $\begin{array}{l}T=1.6\sec .\\ g=9.8m/{\sec }^2\end{array}$

  $\begin{array}{l}1.6=2\pi \sqrt{\frac{l}{9.8}}\\ \frac{1.6}{2\pi }=\sqrt{\frac{l}{9.8}}\\ \frac{0.8}{\pi }=\sqrt{\frac{l}{9.8}}\\ \frac{0.8}{\pi }=\sqrt{\frac{l}{9.8}}Squaringbothsides\\ \frac{0.64}{{\pi }^2}=\frac{l}{9.8}\\ \frac{0.64}{{\pi }^2}\times 9.8=l\\ l=0.635486\\ l=0.64meters\end{array}$

Hence, $l=0.64meters$ .