Final answer:
When the distance from the center of the Earth is doubled, the weight of an object is divided by 4 due to the inverse square law of gravitation.
Step-by-step explanation:
The weight of a body is a measure of the gravitational pull on that body by the Earth and is inversely proportional to the square of the distance from the Earth's center. Therefore, if the distance of a body from the center of the Earth is increased by a factor of 2, the weight of the body will be affected by the square of that factor. The new weight will be inversely proportional to (2)^2, which is 4.
Mathematically, if the original weight is W and the distance is doubled, the new weight W' can be expressed as W' = W / (2)^2 = W / 4. As such, the weight of the body is divided by 4 when the distance is multiplied by 2. This is representative of the inverse square law in gravitation, which dictates how gravitational force—and therefore weight—diminishes with increasing distance from a gravitational source like Earth.