Chapter 10, Problem 73RPP

To determine

The expression that represents the magnitude of the restoring force that the Earth exerts on an object having mass $m$

that is placed at a distance $r$

from the center of the Earth. Note that $\rho$

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

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

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

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

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

e. $mgr$