Question #03b84

1 Answer
Aug 5, 2015

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)