Gravitational force on a particle due to different type of objects

[shauns87]

Homework Statement

A particle is to be placed, in turn, outside four objects, each of mass m: (1) a large uniform
solid sphere, (2) a large uniform spherical shell, (3) a small uniform solid sphere,
and (4) a small uniform shell. In each situation, the distance between the particle and
the center of the object is d. Rank the objects according to the magnitude of the gravitational
force they exert on the particle, greatest first.

Homework Equations

F= Gm1m2/r2

The Attempt at a Solution

As per the shell theorem, a uniform shell of matter attracts a particle that is outside the shell as if all the shell's mass were concentrated at its center. So, as per this theorem, the solid sphere and the shell should exert the same amount of force of the particle. However, a smaller size sphere would exert a lesser force.

 

[jedishrfu]

In each case, the shell theorem reduces the problem to a point of mass m and since all are of mass m then they all exert the same force a given distance from the center sphere/shell objects.

What can you say about the test particle distance from the objects?