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)

$\frac{g}{5}$

Answer 2

Acceleration due to gravity $g = \frac{GM}{R^{2}}\therefore$

$\frac{g_{moon}}{g_{earth}} = \frac{M_{moon}}{M_{earth}}.\frac{R_{earth}^{2}}{R_{moon}^{2}} = \left( \frac{1}{80} \right)\left( \frac{4}{1} \right)^{2}$

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