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