Chapter 14.1, Problem 6PP

To determine

Length of the pendulum on the Moon.

Answer to Problem 6PP

  $16cm$

Explanation of Solution

Given information:

Period of the pendulum, $T=2.0s$

Acceleration due to gravity on Moon, $g$

  $=1.6m/s²$

Formula used:

The period of pendulum is

  $T=2\pi \sqrt{\frac{l}{g}}$

Here, l is the length of the pendulum and g is the acceleration due to gravity.

Calculation:

The time period of a pendulum with the length $l$ is

  $T=2\pi \sqrt{\frac{l}{g}}$

Here, $T$ $=2\mathrm{s}$ $,g$ $=1.6m/s²$

Now, substitute the values and solve:

  $2=2\pi \sqrt{\frac{l}{1.6}}$

Divideboth sides by $2\pi$

  $\frac{1}{\pi }=\sqrt{\frac{l}{1.6}}$

Squareboth sides

  $\frac{1}{\pi ²}=\sqrt{\frac{l}{1.6}}$

Multiplyboth sides by $1.6$

  $\frac{1.6}{\pi ²}=l$

  $l$

  $\begin{array}{l}=\frac{1.6}{\pi ²}\approx 0.16m\\ =16cm\end{array}$

( $0.16m\times 100=16cm$ )

Conclusion:

Thus, the length of a pendulum on the Moon be $16cm$ .