Question

What will be the acceleration due to gravity on the surface of moon if its radius is ${\frac{1}{4}}^{th}$ the radius of the earth and its mass is ${\frac{1}{80}}^{th}$ the mass of earth?

• A. $\frac{g}{2}$
• B. $\frac{g}{3}$
• C. $\frac{g}{7}$
• D. $\frac{g}{5}$

Answer 1

Answer: (D)

$\frac{g}{5}$

We know, $g=\frac{G{M}_e}{{R_e}^2}$
and $g^{\prime }=\frac{G{M}_m}{{R_m}^2}$
$\therefore \frac{g^{\prime }}{g}=\frac{M_m}{M_e}(\frac{R_e}{R_m}{)}^2$
$=\frac{1}{80}\times (\frac{4}{1}{)}^2=\frac{1}{5}$
$\Rightarrow g^{\prime }=\frac{g}{5}$