Chapter 4.2, Problem 23SSC

To determine

Comparison of force holding arock on earth and moon.

Answer to Problem 23SSC

Force required to hold the rock on earth is 6.125 times greater than the force required to hold the rock on moon.

Explanation of Solution

Given:

Mass of the rock, $m=10\text{ kg}$

Gravitational field on the moon, $g_m=1.6\text{ N/kg}$

Formula Used:

Force required to hold the rock:

  $F=mg$

Here, m is mass and gis acceleration due to gravity.

Acceleration due to gravity on earth is $g=9.8\text{ kg}\cdot {\text{m/s}}^2$

Calculations:

Force required to hold the rock on Earth is:

  $\begin{array}{c}F=10\times 9.8\\ =98\text{ N}\end{array}$

So, the force required to hold the rock on earth is 98 N

Now, gravitational field on moon is $g_m=1.6\text{ N/kg}$

Force required to hold the rock on moon is:

  $F=m{g}_m$

Here, m is mass and $g_m$ is acceleration due to gravity on moon.

Therefore,

  $\begin{array}{c}{F}_m=10\times 1.6\\ =16\text{ N}\end{array}$

So, force required to hold the rock on earth is 16 N.

Now, ratio of required forces on earth and moon is:

  $\begin{array}{l}\frac{F}{F_m}=\frac{98}{16}\\ F=6.125F_m\end{array}$

Conclusion:

Therefore, force required to hold the rock on earth is 6.125 times greater than force required to hold the rock on moon.