Chapter 7.2, Problem 20SSC

To determine

Strength of $g$ on Moon’s surface.

Answer to Problem 20SSC

  $g=1.528\text{N/kg}$

Explanation of Solution

Given:

Mass of moon is $m=7.3\times {10}^{22}\text{kg}$

Radius of Moon is $r=1.785\times {10}^6\text{m}$

Formula Used:

Strength of gravitational field is given as $g=\frac{Gm}{r^2}$   …..     (1)

  $G$ is gravitational constant equal to $6.67\times {10}^{-11}{\text{N-m}}^2{\text{/kg}}^{\text{2}}$

Calculations:

From (1)

  $g=\frac{Gm}{r^2}$

Putting the values

  $\begin{array}{l}g=\frac{6.67\times {10}^{-11}\times 7.3\times {10}^{22}}{{\left(1.785\times {10}^6\right)}^2}\\ =1.528\text{N/kg}\end{array}$

Conclusion:

Value of $g$ on Moon’s surface is $g=1.528\text{N/kg}$