Question

Find a numerical value for rhoearth, the average density of the earth in kilograms per cubic meter. Use 6378km for the radius of the earth, G=6.67×10−11m3/(kg⋅s2), and a value of g at the surface of 9.80m/s2.

Answer 1

5499.5 kg/m³

Step-by-step explanation:

Parameters given :

Acceleration due to gravity, g = 9.8 m/s²

Gravitational constant, G = 6.67 * 10^(-11) m3/kgs²

Radius of earth, R = 6378 km = 6.378 * 10^6 m

Density is given as:

ρ = mass/volume

To get the mass of earth, M, in terms of acceleration due to gravity, g, and gravitational constant, G:

g = (G*M) / R²

Making M subject of formula:

M = (R² * g) / G

The earth is regarded as a sphere, hence, the volume of the earth is:

V = 4/3 * pi * R³

Therefore:

ρ = (R² * g) / G ÷ 4/3 * pi * R³

ρ = [(R² * g) / G] * [3/(4 * pi * R³)]

ρ = (R² * g * 3) / (G * 4 * pi * R³)

ρ = (3 * g) / (4 * G * pi * R)

ρ = (3 * 9.8) / (4 * 6.67 * 10^(-11) * 3.142 * 6.378 * 10^6)

ρ = 5499.5 kg/m³