The Mystery of Weight and Distance Relationship

What happens to the weight of an object when the distance from the center of the Earth is doubled?

A. The weight is multiplied by 4.
B. The weight is divided by 4.
C. The weight is divided by 2.
D. The weight is multiplied by 2.
Final answer:

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.

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.