Chapter 7, Problem 64A

To determine

To Write:A physics problem for the given equation.

Explanation of Solution

Introduction:

The given equation is:

  $8.3\times {10}^3\text{m/s=}\sqrt{\frac{\left(6.67\times {10}^{-11}\text{N}\cdot {\text{m}}^{\text{2}}{\text{/kg}}^2\right)\left(5.97\times {10}^{24}\text{kg}\right)}{r}}$

Here, $6.67\times {10}^{-11}\text{N}\cdot {\text{m}}^{\text{2}}{\text{/kg}}^2$ is the universal gravitational constant (G) and $5.97\times {10}^{24}\text{kg}$ is the mass of the earth (M).

The mathematical formula to obtain orbital velocity of a satellite is:

  $v=\sqrt{\frac{GM}{r}}$

Where, G is the gravitational constant, M is the mass of the planet and r is the distance of the satellite from the center of the planet.

The physics problem for the given equation can be:

Calculate the orbital radius of satellite revolving about the earth which has an orbital velocity of $8.3\times {10}^3\text{m/s}$ .

To solve this, the mathematical formula or orbital would be used and known values would be substituted. On re-arranging formula, orbital radius of the satellite would be calculated.