Question

The earth?s mass is $80$ times that of moon and their diameters are $1600 \,km$ and $800 \,km$ , respectively. If $g$ is the value of acceleration due to gravity on earth, what is its value on moon?

• A. $g$
• B. $g/2$
• C. $g/10$
• D. $g/20$

Answer 1

Answer: (D)

$g/20$

Answer 2

Acceleration due to gravity on earth,
$g=\frac{GM_{e}}{R_{e}^{2}}$
$=\frac{G\times80M_{m}}{\left(800\right)^{2}}$
$=\frac{GM_{m}}{8\times10^{3}} \ldots\left(i\right)$
Acceleration due to gravity on moon,
$g_{m}=\frac{GM_{m}}{R_{m}^{2}}$
$=\frac{G\times M_{m}}{\left(400\right)^{2}}$
$=\frac{GM_{m}}{160\times10^{3}}$
$\therefore g_{m}=\frac{8g}{160}$
$\Rightarrow g_{m}=\frac{g}{20}$ (using (i))