Chapter 7.2, Problem 23SSC

To determine

The strength of the gravitational field of Earth where an astronaut experiences a $25\%$ reduction in its weight.

Answer to Problem 23SSC

  $7.35{\text{m/s}}^{\text{2}}$

Explanation of Solution

Given:

The mass of the astronaut is $80\text{-kg}$ and there is a reduction of $25\%$ in its weight.

Formula used:

Weight of an object of mass $m$ is given by:

  $W=mg$

Where, $g$ is the strength of the Earth’s gravitational field.

Calculation:

Let the strength of the Earth’s gravitational field at the given point be $g\text{'}$ . Then, it is given that there is a 25% reduction in weight of the astronaut at that point. Thus, it can be written as,

  $\begin{array}{l}W\text{'}=75\%\left(W\right)\\ mg\text{'}=\frac{75}{100}\left(mg\right)\\ g\text{'}=0.75\left(g\right)\end{array}$

Using the known value of $g=9.8{\text{m/s}}^{\text{2}}$ in above,

  $\begin{array}{c}g\text{'}=0.75\left(9.8\right)\\ =7.35{\text{m/s}}^{\text{2}}\end{array}$

Conclusion:

Thus, the strength of the gravitational field at the considered point is $7.35{\text{m/s}}^{\text{2}}$ .