Gravitational force on a particle due to different type of objects

In summary, a test particle is placed outside four objects of mass m - a large uniform solid sphere, a large uniform spherical shell, a small uniform solid sphere, and a small uniform shell - at a distance d from their centers. According to the shell theorem, the gravitational force exerted by the solid sphere and the shell on the particle would be the same. However, a smaller sized sphere would exert a lesser force. Therefore, the objects can be ranked in terms of the magnitude of gravitational force they exert on the particle, with the largest force being exerted by the large uniform solid sphere, followed by the large uniform spherical shell, the small uniform solid sphere, and the small uniform shell. The distance between the particle and the objects is
  • #1
shauns87
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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.
 
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  • #2
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?
 

1. What is gravitational force?

Gravitational force is a natural phenomenon by which all objects with mass are attracted towards one another.

2. How is gravitational force calculated?

The gravitational force on a particle is calculated by multiplying the mass of the particle by the acceleration due to gravity.

3. What types of objects can exert gravitational force on a particle?

Any object with mass, regardless of its size or composition, can exert gravitational force on a particle.

4. How does the distance between objects affect gravitational force?

The gravitational force between two objects decreases as the distance between them increases. This is described by the inverse square law.

5. Can different types of objects have different gravitational forces on a particle?

Yes, the gravitational force on a particle can vary depending on the mass and distance of the object exerting the force. For example, the gravitational force on a particle due to a planet will be greater than the gravitational force due to a smaller object like a star.

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