Question

the earth mass is 80 times that of moon on and their diameter are in the ratio of 4:1 respectively what is the value of g on moon

Answer 1

The Earth's mass is 80 times that of the moon and their diameters are in the ratio of 4;1. What is the value of acceleration due to gravity g on moon





Say, the acceleration due to gravity on moon is g '  and  that on earth is g.
We know that,
g = GM/R2
where,
G > gravitation constant
M > mass of earth
R > radius of earth
let us introduce a new parameter, D = diameter of earth = 2R
=> R = D/2 

so,
g '= 4GM/D2................(1)

also,
g ' = Gm/r2
where,
G > gravitation constant
m > mass of moon
r > radius of moon
let us introduce a new parameter, D = diameter of moon = 2r
=> r = d/2 

so,
g '= 4Gm/d2................(2)

Now, 
it is given,
M:m = 80:1
as Earth's  mass is 80 times moon's.
and,
D:d = 4:1
as their diameters are in the given ration in the question.

by deviding equation 1 by 2,
(1)/(2) 

g/g '  
=  [4GM/D2]/[4Gm/d2]
=  [M/D2]/[m/d2]
=  [M:m]*[d2:D2]
=  ​[M:m]/[D:d]2
=  [80/1]/[4/1]2
=  (80)/(16)
=  5

Now,
we have,
g:g ' = 5:1
so,
g ' = g/5
= 9.81/5
= 1.9802
≈ 1.98 m/s2

Answer 2

ANSWER BY USING THE FORMULA
.................
formula, 

g=GM/R^2 
$= = = = = = = = =$

substituting values we get, 
ge/gm=

(M/R^2)/ (M/r^2). 

10/gm = (80m/16r^2)/ (M/r^2) 

solving these we get, 

gm= 2m/s^2