Answer to Question #276860 in Classical Mechanics for gelo

Question

Compute the mass of the earth, assuming it to be a sphere of radius 6.37 x 10^6 m.

Answer 1

Let's first find the volume of Earth:

$$V=\dfrac{4}{3}\pi r^3.$$

Finally, we can find the mass of Earth from the definition of the density:

$$\rho=\dfrac{m}{V},$$ $$m=\rho V=\dfrac{4}{3}\pi\rho r^3,$$ $$m=\dfrac{4}{3}\times\pi\times5510\ \dfrac{kg}{m^3}\times(6.37\times10^6\ m)^3=5.97\times10^{24}\ kg.$$