A particle might be placed:. 1. inside a uniform spherical shell of mass M, but not at the center
2. inside a uniform spherical shell of mass M, at the center
3. outside a uniform spherical shell of mass M, a distance r from the center
4. outside a uniform solid sphere of mass M, a distance 2r from the center
Rank these situations according to the magnitude of the gravitational force on the particle, least to greatest.
A) All tie
B) 1, 2, 3, 4
C) 1 and 2 tie, then 3 and 4 tie
D) 1 and 2 tie, then 3, then 4
E) 1 and 2 tie, then 4, then 3

D) 1 and 2 tie, then 3, then 4.

Explanation: Gravitational Force is one of the 4 fundamental forces of nature (the others being eletromagnetic, weak force and strong force) and is explained by Newton's Law of Universal Gravitation, in which, every massive particle attracts every other massive particle.

The way to calculate gravitational force is:

G is Universal Gravitational Constant and it is constant anywhere in the universe.

M and m are mass of each object;

r is distance between the objects;

The formula shows that gravitational force acts at an inverse square law, i.e., if objects are 2 distances apart, Force between them will decrease to one quarter of it was.

So, analysing the question, a particle inside an uniform spherical shell not at the center and at the center will have equal forces.

Outside at a distance 2r, force will be less than at a distance r.

Then the order is 1=2 > 3 > 4

explanation:

could i give you a exaplo that could you?

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.