Question

if the radius of Earth were to be increased by a factor of 3, by what factor would is density have to be changed to keep g the same?​

Answer 1

Explanation:

The acceleration due to gravity g = G x M/R²

here G = Gravitational constant

M = mass of earth

R = radius of earth

The value of g can also be written as g = G x 4/3 πR³ρ /R²

here ρ is the density of earth

Thus g = G x 4/3 π R ρ

From this relation if R is made three times . The ρ is to made 1/3 times , so hat the value of g remains the same .