Final answer:
The force of gravity on the meteorite will increase by a factor of 16 when it is one-quarter the distance from the center of the Earth, resulting in a new gravitational force of 8.0 × 10^5 N.
Step-by-step explanation:
The force of gravity on an object is given by Newton's Universal Law of Gravitation, F = GMm/r^2, where F is the gravitational force, G is the gravitational constant, M and m are the masses of the two objects, and r is the distance between their centers. In this scenario, when the meteorite reaches a point one-quarter of the initial distance from the center of the Earth, the gravitational force can be calculated by reducing the distance r in the formula to r/4, which, when squared, becomes r^2/16. As a result, since the distance is reduced to a quarter, the gravitational force increases by a factor of 16. So the new gravitational force will be 16 × 5.0 × 10^4 N, which equals 8.0 × 10^5 N.