Question

If the acceleration due to gravity at earth is g and mass of earth is 80 times that of moon and radius of earth is 4 times that of moon ,then what is the value of 'g' at the surface of 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
then
we have,
g:g ' = 5:1
so,
g ' = g/5
= 9.81/5
= 1.9802
≈ 1.98 m/s2 ans

i hope its hlp you