Final answer:
A body weighing 200 N on the surface of the Earth will weigh 50 N when it is halfway to the Earth's center, by applying the formula W' = W × (r/R)^2 with r = R/2. This calculation is based on Newton's Law of Universal Gravitation, which factors in only the mass enclosed within the radius r. The provided options do not include the correct answer, indicating a potential misprint.
Step-by-step explanation:
The question at hand is a Physics problem related to gravitational force within the Earth. Newton's Law of Universal Gravitation indicates that the gravitational force inside a spherical shell of uniform density is zero. Thus, for a body located at a distance r from the center of the Earth, which has a radius of R, only the mass enclosed within that radius contributes to the gravitation attraction. We can use the following equation to find the new weight:
W' = W × (r/R)^2
Where W' is the new weight, W is the weight on the surface, r is the distance from the center of the Earth, and R is the Earth's radius. Therefore, halfway to the center, r = R/2 and:
W' = 200 N × (1/2)^2 = 200 N × 1/4 = 50 N
However, since this option is not available in the question provided, it could be a misprint, or the question may be expecting the use of the answer (a) 100 N assuming linear variation, which is incorrect for a spherical mass distribution.