As you go down into a deep well or mine shaft from the surface of the Earth, what happens to your weight (the gravitational force acting on you)?

Introduction / Context:
Weight is the gravitational force that the Earth exerts on a body of a given mass. Many conceptual physics questions explore how weight changes with altitude above the Earth or depth below the surface. This question specifically considers what happens to a person weight when moving down into a deep well or mine shaft compared with staying on the surface.

Given Data / Assumptions:

• The situation is going down from the Earth surface into a well or mine.

• Mass of the person is assumed to remain constant.

• Only the change in gravitational acceleration g with depth is considered.

• The depth is small compared with the Earth radius, but not negligible in concept.

Concept / Approach:
Gravitational force on a body of mass m at distance r from the Earth centre is given by F = G * M * m / r² for points outside a spherically symmetric mass. Inside the Earth, only the mass enclosed within radius r contributes to gravity, and the effective gravitational acceleration decreases with depth. For small depths compared with the Earth radius, g decreases approximately linearly as one moves towards the centre. Therefore, as you go down into a well or mine, your weight, which equals m * g, decreases slightly compared with its value at the surface.

Step-by-Step Solution:
Step 1: Recall that weight W is given by W = m * g, where m is mass and g is gravitational acceleration. Step 2: Understand that as you move below the surface, you are effectively inside the Earth mass distribution. Step 3: Inside a uniformly dense sphere, gravitational acceleration decreases with decreasing radius because outer shells of mass do not contribute to the net force at that point. Step 4: Apply this idea to the Earth and note that although the density is not perfectly uniform, the general trend of g is to decrease as depth increases below the surface. Step 5: Conclude that since m is constant and g is slightly smaller, your weight decreases slightly as you go down into a well.

Verification / Alternative check:
Advanced treatments in physics texts show that near the Earth surface, g decreases both as you move above the surface (to higher altitude) and as you move below it (into deep mines), though the reasons differ. Experimental measurements in deep mines confirm that the value of g is slightly less than at the surface. For small depths relative to the Earth radius, the change is small but measurable. These results support the statement that weight decreases slightly with depth below the surface.

Why Other Options Are Wrong:
The option it increases slightly would be true only if more mass were pulling you from below, but due to the shell property of gravitation, outer layers of the Earth do not increase the net pull when you are inside them. It remains exactly the same is incorrect because careful measurement and theory both show variation of g with position. None of these is too vague and does not match the known physical behaviour. The statement it first increases then becomes zero at the centre is also not correct for small depths; for an idealised Earth with uniform density, g decreases steadily from the surface to the centre.

Common Pitfalls:
Many students intuitively think that getting closer to the Earth centre must increase gravity, forgetting that mass above the observation point does not contribute to the net force. Some also confuse the situation with moving above the surface, where g definitely decreases, but assume the opposite below the surface. To avoid these misunderstandings, it is useful to remember that inside a symmetric body, gravitational acceleration is proportional to the distance from the centre and therefore becomes smaller as one moves deeper underground.

Final Answer:
As you go down into a well or mine shaft, your weight decreases slightly compared with its value at the surface.