By applying Newton's Universal Law of Gravitation and rearranging it to solve for the distance r, we calculate the distance from the center of Earth, using the given force and masses, to be 4.4 x 10^7 meters.
The question requires us to use Newton's Universal Law of Gravitation to calculate the distance of an object from the center of Earth given the force acting on it. This law is given by the equation F = G * (m1 * m2) / r^2, where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two masses. We are given F (5.25 N), G (6.6737 x 10^-11 N m^2/kg^2), the object's mass (25.5 kg), and Earth's mass (5.98 x 10^24 kg).
By rearranging the formula to solve for r we get r = sqrt(G * m1 * m2 / F). Substituting the given values into this equation, we can calculate r. After computation, we conclude that the correct distance from the center of Earth is option b) 4.4 x 10^7 meters, which matches with provided answer choices.