Chapter 5, Problem 32P

To determine

The acceleration due to gravity on a hypothetical planet surface.

Answer to Problem 32P

Solution:

The acceleration due to gravity on a hypothetical surface is $2.45{\text{m/s}}^{\text{2}}$ .

Explanation of Solution

Given:

Planet has a radius 2 times that of the Earth.

Formula Used:

Acceleration due to gravity on the surface is given by:

  $g=\frac{Gm}{r^2}$

Where, m is the mass of the planet and r is its radius.

Calculation:

Let the mass of the earth be m and radiusr .

If the mass of the new planet be m’ and radius be r’ .

Acceleration due to gravity on earth’s surface is $9.8{\text{m/s}}^{\text{2}}$ .

If the acceleration due to gravity on the new planet is g’ .

  $\begin{array}{l}\frac{g\text{'}}{g}=\frac{Gm\text{'}/r{\text{'}}^2}{Gm/r^2}\\ m\text{'}=m\\ r\text{'}=2r\\ \frac{g\text{'}}{g}=\frac{r^2}{r{\text{'}}^2}\\ g\text{'}=\frac{r}{{\left(2r\right)}^2}g\\ g\text{'}=\frac{g}{4}\\ g\text{'}=\frac{9.8{\text{m/s}}^{\text{2}}}{4}\\ g\text{'}=2.45{\text{m/s}}^{\text{2}}\end{array}$

Conclusion:

Hence, the acceleration due to gravity on a hypothetical surface is $2.45{\text{m/s}}^{\text{2}}$ .