Info is quite incorrect, as instead of 80, it is 96.
Let radius of moon= [tex]r_m [/tex]
radius of earth= [tex]r_e[/tex]
mass of moon= [tex]m_m[/tex]
mass of earth= [tex]m_e[/tex]
Let acc. due to gravity on earth= [tex]g_e[/tex]
acc. due to gravity on moon= [tex]g_m[/tex]
Given, [tex]r_e=4r_m[/tex] and [tex]m_e=96m_m[/tex]
We know,
[tex]g_e= \frac{Gm_e}{r_e^2} [/tex] ............(i)
So,
[tex]g_m= \frac{Gm_m}{r_m^2} [/tex] ...........(ii)
Where G is the Universal gravitational constant
Divide (i) by (ii)
[tex] \frac{g_e}{g_m} = \frac{Gm_e}{r_e^2} * \frac{r_m^2}{Gm_m} [/tex]
[tex] \frac{g_e}{g_m} = \frac{m_e}{r_e^2} * \frac{r_m^2}{m_m} [/tex]
Substitute the values-:
[tex] \frac{g_e}{g_m} = \frac{96m_m}{(4r_m)^2} * \frac{r_m^2}{m_m} [/tex]
[tex]\frac{g_e}{g_m} = 6[/tex]
[tex]g_m= \frac{g_e}{6} [/tex]
We know, [tex]g_e=9.8m/s^2[/tex]
So, [tex]g_m= \frac{9.8}{6} = 1.633 m/s^2[/tex]
