Chapter 10, Problem 60GP

* Traveling through Earth A hole is drilled through the center of Earth The gravitational force exerted by Earth on an object of mass m as it goes through the hole is mg $(r/R)$, where r is the distance of the object from Earth’s center and R is the radius of Earth $\left(\text{6}\text{.4 }\times {\text{ 10}}^{\text{6}}\text{m}\right)$. Will an object dropped into the hole execute simple harmonic motion? if yes, find the period of the motion Would this be a comfortable ride? How does one-half of this time compare with the time needed to fly in an airplane halfway around Earth? What assumptions did you make to solve the problem?