Question

The Earth’s average radius is 6400 km and its average density is 5.5 g/cm3. If all of the Earth’s matter were compressed to the density of the atom calculated above, what would be the radius of the Earth? Answer in units of m.

Answer 1

Explanation:

Radius of Earth, $r=6400\ km=64\times 10^5\ m$

Average density, $d=5.5\ g/cm^3=5500\ kg/m^3$

Density is given by :

$d=\dfrac{m}{V}$

$d=\dfrac{m}{(4/3\pi r^3)}$

$d=\dfrac{3m}{4\pi r^3}$

$r^3=\dfrac{3m}{4\pi d}$

$r^3=\dfrac{3m}{4\pi d}$

m is the mass of earth, $m=5.97\times 10^{24}\ kg$

$r^3=\dfrac{3\times 5.97\times 10^{24}}{4\pi \times 5500}$

$r=6375131.35\ m$

or

$r=6.37\times 10^6\ m$

So, the radius of the Earth is $6.37\times 10^6\ m$. Hence, this is the required solution.