Chapter 7, Problem 4STP

To determine

To Choose: The correct option.

Answer to Problem 4STP

C. $1.2\pi \times {10}^3\text{}\text{s}$

Explanation of Solution

Given:

The distance of the moon from the center of the planet is $5.43\times {10}^6\text{m}$ .

Orbital speed of moon, $v=9.0\times {10}^3\text{m/s}$

Formula used:

The time period of an object in circular motion of radius $r$ with speed $v$ is given by:

  $\begin{array}{c}T=\frac{\text{Distance}}{\text{Speed}}\\ =\frac{2\pi r}{v}\end{array}$

Calculation:

Using the given values of radius of the circle and the velocity of the moon, the time period of the moon around the planet can be calculated as follows:

  $\begin{array}{c}T=\frac{2\pi r}{v}\\ =\frac{2\pi \times 5.43\times {10}^6}{9.0\times {10}^3}\\ =1.2\pi \times {10}^3\text{}\text{s}\end{array}$

Conclusion:

Thus, time period of the moon around the planet is $1.2\pi \times {10}^3\text{}\text{s}$ .