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 $g=\frac{GM}{R^2}$

$\therefore \frac{g_{\text{moon}}}{g_{\text{earth}}}=\frac{M_{\text{moon}}}{M_{\text{earth}}}.\frac{R_{\text{earth}}^2}{R_{\text{moon}}^2}$

$=(\frac{1}{80})(\frac{4}{1}{)}^2$

$g_{\text{moon}}=g_{\text{earth}}\times \frac{16}{80}=\frac{g}{5}$