Chapter 10, Problem 72RPP

To determine

The expression that represents the mass $m$

of the Earth that is inside a sphere of radius $r$

that is smaller than the radius $R$

of the Earth. Note that $\rho$

is the density of the Earth which is assumed uniform. The following options are given:

a. $\left(\frac{4}{3}\right)\pi r^3\rho$

b. $G\left(\frac{4}{3}\right)\pi r^3\rho$

c. $\frac{G{M}_{\text{Earth}}}{r^2}$

d. $G\left(\frac{4}{3}\right)\pi r\rho$

e. $mg$