Question

What is the value of acceleration due to gravity on the moon?

• A. $\frac{g}{4}$
• B. $\frac{g}{5}$
• C. $\frac{g}{6}$
• D. $\frac{g}{2}$

Answer 1

The correct option is C $\frac{g}{6}$

Since on the Earth, $g=\frac{GM}{R^2}$​
Similarly for the moon, $g_{moon}$ ​= $\frac{G{M}_{moon}}{{\left(R_{moon}\right)}^2}$​
$M_{moon}$ ​and $R_{moon}$​ are the mass and radius of the moon respectively

$\frac{g}{g_m}=\frac{M/R^2}{M_{moon}/R_{moon}^2}$
Now, by putting the values we get:
$\frac{g}{g_m}=\frac{5.972\times {10}^{24}kg\times (1731km{)}^2}{7.3\times {10}^{22}kg\times (6371km{)}^2}$
$\frac{g}{g_m}\approx 6$
$g_m=\frac{g}{6}$​