Question

How does the value of 'g' on the earth is related to the mass of the earth and its radius? derive it .

Answer 1

the ans is 10 m/s sq
g = Gm
r2

Answer 2

Let mass of earth be M
mass of the body m
force of attraction between them F
and distance between earth and the body from centre of earth r

According to newton's universal law of gravitation
F=G(M*m/r^2) - (1)
and also according to newton's second law of motion F=mg - (2) {m is mass and g is acceleration due to gravity}

substituting equation (2) in (1)

mg=G(M*m/r^2)
g=G(M*m/r^2)/m
(m cancels m)

leaving

g=GM/r^2

so g is related to M that is mass of earth and radius of earth that is r.
sorry