Question

If the radius of the earth were increased by n factor 2 keeping the mass constant, by what factor would its density have to be changed to keep g the same?​

Answer 1

Answer:

the formula for calculating the density of the earth is given as

ρ = M /V = [gR^2 / G] / [(4/3)πR^3]

as g = GM/R^2 and V = (4/3)πR^3

so,

ρ = (3/4).(g / πRG)

now, if the radius is increased, the new density will be given as

ρ' = (3/4).(g / πR'G)

now as

R' = 3R

so,

ρ' = (3/4).(g / π(3R)G)

so,

ρ' = (1/3).(3/4).(g / πRG)

thus,

ρ' = (1/3)ρ

so, the new density would decrease to one-third its initial value.

Explanation: