Final answer:
The force of gravity on an object at a distance of 12,740 km from the center of Earth would be one-quarter of the force experienced on Earth's surface due to the inverse-square law of universal gravitation; thus, the correct answer is B. 200 N.
Step-by-step explanation:
If an object has a force of gravity of 800 N on Earth's surface, we can determine the force of gravity on the same object at a distance of 12,740 km from the center of Earth using Newton's law of universal gravitation, given the gravitational constant G = 6.674 × 10^{-11} N·m^2/kg^2 and the mass of Earth M = 5.97 × 10^{24} kg. The force of gravity is inversely proportional to the square of the distance from the center of Earth, so if the distance from the center is doubled, the gravitational force is reduced by a factor of four. Given that the radius of Earth is approximately 6.38 × 10^6 m, moving to a distance of 12,740 km (which is twice the Earth's radius, as 12,740,000 m is approximately two times 6.38 × 10^6 m) would imply that the gravitational force should be reduced to a quarter of the force experienced on the surface. Therefore, the object would experience a force of 800 N / 4 = 200 N at a distance of 12,740 km from the center of Earth. The correct answer is B. 200 N.