ques abt gravity...?

Question

i have given 3 cases below. I just want you to explain, in which of the cases will my weight be the maximum..

1). i am standing on earths surface
2). i am standing 200m the earths crust
3). i am standing 200m away from the earths crust in the atmosphere....

Answer 1

If you approximate the Earth as a sphere of uniform density and radius R, (it's nearly a sphere, but doesn't really have uniform density), the gravity as a function of distance from the center is like this:

g is proportional to 1/r^2 outside the Earth
g is proportional to r inside the Earth

In layman's terms, the gravity at the center is zero. As you go up toward the surface, the gravity steadily increases. As you keep going up, the gravity reaches a maximum at the surface, then starts decreasing as your altitude increases.

So, the answer to your question is 1)...unless they want you to take into account the variable density, in which case it's probably 2).

Answer 2

In case 1 you weight the most - you are as far away from the center as you can be while having all of the mass of the earth below and still being in contact with hte earth.

In case 2, the mass of the earth above you does not pull "down" on you, so the mass of earth is reduced (a little) and your weight is reduced (a little)

In case 3 you are moving farther away from the center but not adding any more mass to that already below. Hence the force starts to fall off like 1/r^2 and you weight decreases (a little).

Answer 3

If the Earth were a uniform sphere, the answer would be (1). However, the Earth is not a uniform sphere; it increases rapidly in density towards the center. Therefore the answer is (2) assuming you meant "I am standing 200m below the earth's crust."