Question

The moon's radius is $\frac{1}{4}$ th that of the earth & its mass is $\frac{1}{80}$ times that of earth, if $g$ represents the acceleration due to gravity on the surface of earth, that on the surface of moon is -

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

Answer 1

Answer: (B)

We know gravitational acceleration
$g=\frac{G M}{R^{2}}$
for moon $R_{m}=\frac{1}{4}R \, \& \, M_{m}=\frac{M}{80}$
so $g^{'}=\frac{G \left(\right. \frac{M}{80} \left.\right)}{\left(\right. \frac{R}{4} \left.\right)^{2}}=\frac{G M}{5 R^{2}}=\frac{g}{5}$