Question

Question #03b84

Answer 1

`rho_(earth)=(3g)/(4G*pi*R)`

Just don't forget that `d_(earth)=(rho_(earth))/(rho_(water))` and `rho_(water)=1000kg`/`m^3`

Explanation:

Knowing that a body's density is calculated as:

`"body's volumic mass"/"water's volumic mass"`

Knowing that water's volumic mass expressed in `kg`/`m^3` is `1000`.

In order to find earh's density, you need to calculate
`rho_(earth)=M_(earth)/V_(earth)`

Knowing that `g=(G*M_(earth))/((R_(earth))^2) rarr g/G=(M_(earth))/((R_(earth))^2)`

A sphere's volume is calculated as:
`V=4/3*pi*R^3=4/3*pi*R*(R^2)`

Therefore:

`rho_(earth)=g/(G*4/3*pi*R)=(3g)/(4G*pi*R)`