Gravitational force on a particle due to different type of objects

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SUMMARY

The discussion focuses on the gravitational force exerted on a particle by four different objects of mass m: a large uniform solid sphere, a large uniform spherical shell, a small uniform solid sphere, and a small uniform shell. According to the shell theorem, both the large solid sphere and the large spherical shell exert the same gravitational force on the particle when placed at a distance d from their centers. Conversely, the smaller solid sphere and the smaller shell exert a lesser gravitational force due to their reduced mass distribution. Thus, the ranking of gravitational force from greatest to least is: large solid sphere = large spherical shell > small solid sphere = small spherical shell.

PREREQUISITES
  • Understanding of Newton's Law of Universal Gravitation
  • Familiarity with the Shell Theorem
  • Basic knowledge of gravitational force equations (F = Gm1m2/r²)
  • Concept of mass distribution in solid and shell objects
NEXT STEPS
  • Study the Shell Theorem in detail to understand its implications in gravitational physics.
  • Explore gravitational force calculations for different mass distributions.
  • Learn about the effects of distance on gravitational force in various scenarios.
  • Investigate real-world applications of gravitational force in astrophysics.
USEFUL FOR

Students of physics, educators teaching gravitational concepts, and anyone interested in understanding the principles of gravitational forces and their applications in different mass configurations.

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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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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?
 

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