Question

(a) If a hole could be dug to the center of the Earth, would the force on an object of mass m still obey Equation 13.1 there? (b) What do you think the force on m would be at the center of the Earth?

Short answer

This equation does not take care of the situation of a hole drilled through our Earth.

Step-by-step solution

Universal Gravitational force.

The Law of Universal Gravitation states that every point mass attracts every other point mass in the universe by a force pointing in a straight line between the centers-of-mass of both points.

And this force is proportional to the masses of the objects and inversely proportional to their separation

Explanation of the force

$F_g=G\left(\frac{M_1{m}_2}{R^2}\right)$

At the center of Earth, symmetry demands that the force vanish. However, if we just blindly plug-in R = 0 into Newton's Law of Universal Gravitation we get an undefineddivision by zero.

So either of those results tells us that this equation does not take care of the situation of a hole drilled through our Earth.