Understanding the Relationship Between Weight and Distance from Earth's Center
What is the effect on the weight when the distance from Earth's center is multiplied by 2?
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.
Answer:
The correct answer is A. The weight is multiplied by 4 when the distance is multiplied by 2.
The weight of a body above the surface of the Earth is inversely proportional to the square of its distance from the center of the Earth. This means that as the distance increases, the weight decreases, and vice versa. If the distance from the center of the Earth is multiplied by 2, it means that the new distance is twice as much as the original distance.
To determine the effect on the weight, we need to consider the inverse square relationship. When the distance is multiplied by 2, the inverse square of the distance is calculated as (1/(2²)), which simplifies to 1/4. This means that the weight is divided by 1/4, which is the same as multiplying the weight by 4.
Therefore, the correct answer is A. The weight is multiplied by 4 when the distance is multiplied by 2.
In conclusion, when the distance from the center of the Earth is multiplied by 2, the weight is multiplied by 4.