Question #03b84

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Answer 1 · 2015-08-05T09:38:22

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

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

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)#