Question

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

• A. $g/4$
• B. $g/5$
• C. $g/6$
• D. $g/8$

Answer 1

The correct option is B $g/5$

Acceleration due to gravity on the earth's surface is $g=\frac{G{M}_e}{R_e^2}$

Acceleration due to gravity on the moon's surface is $g_m=\frac{G{M}_m}{R_m^2}$

Given, $R_m=\frac{R_e}{4}$ or $\frac{R_m}{R_e}=\frac{1}{4}$ and $M_m=\frac{M_e}{80}$ or $\frac{M_m}{M_e}=\frac{1}{80}$

So, $\frac{g_m}{g}=\frac{M_m}{M_e}\times (\frac{R_e}{R_m}{)}^2=(1/80)\times (4{)}^2=1/5$

or $g_m=g/5$