Question

For the moon, its mass is $\frac{1}{81}$ of earth's mass and its diameter is $\frac{1}{3.7}$ of earth's diameter.If acceleration due to gravity of earth surface is $9.8m/s^2$, then at the moon its value is:

• A. $2.86m/s^2$
• B. $1.65m/s^2$
• C. $8.65m/s^2$
• D. $5.16m/s^2$

Answer 1

The correct option is B $1.65m/s^2$

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

At Earth, $g_e=\frac{G{M}_e}{R_e^2}$,

and at Moon, $g_m=\frac{G{M}_m}{R_m^2}$

$\therefore \frac{g_e}{g_m}=\frac{M_e}{M_m}(\frac{R_m}{R_e}{)}^2$

$\Rightarrow g_m=g_e\times \frac{M_m}{M_e}\times (\frac{R_e}{R_m}{)}^2$

$=9.8\times \frac{1}{81}\times 3.7\times 3.7$

$=1.65$ $m/s^2$