Question

The moon’s radius is $1/4$ that of the earth and its mass is $1/80$ times that of the earth. If $g$ represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is

• A. $\frac{g}{4}$
• B. $\frac{g}{5}$
• C. $\frac{g}{6}$
• D. $\frac{g}{8}$

Answer 1

Answer: (B)

Acceleration due to gravity $g = \frac{GM}{R^2}$
$\therefore \frac{g_{\text{moon}}}{g_\text{earth}} = \frac{M_\text{moon}}{M_\text{earth}} .\frac{R^2_\text{earth}}{R^2_\text{moon}}$
$ =(\frac{1}{80}) (\frac{4}{1})^2$
$g_\text{moon} = g_\text{earth} \times \frac{16}{80} = \frac{g}{5}$