Gravitational Acceleration (Gauss law)

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SUMMARY

The discussion centers on calculating gravitational acceleration using Gauss's law, specifically in the context of Earth's structure. The user interprets R2 as the overall radius of Earth and attempts to compute gravitational acceleration (g) by determining the mass of Earth's core and mantle based on given densities and volumes. The calculated value of g is 4.1, which is incorrect as it does not align with the expected gravitational acceleration at Earth's surface. The user seeks assistance in refining their approach to the problem.

PREREQUISITES
  • Understanding of Gauss's law in physics
  • Knowledge of gravitational acceleration formulas
  • Familiarity with density and volume calculations
  • Basic concepts of Earth's internal structure
NEXT STEPS
  • Review the derivation of gravitational acceleration using Gauss's law
  • Study the relationship between mass, density, and volume in planetary bodies
  • Learn how to accurately apply the formula g = GM/(R^2) in different contexts
  • Examine the structure of Earth, focusing on core and mantle properties
USEFUL FOR

Students studying physics, particularly those focusing on gravitational forces and planetary science, as well as educators seeking to clarify concepts related to Gauss's law and gravitational acceleration.

moknight
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Homework Statement


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Homework Equations



Just to clarify the question, the value given for R2 is the overall radius of Earth, it isn't R1-R2. (At least, that's my interpretation given that the R2 value is approx. the Earth's radius)

The Attempt at a Solution



Don't really know how to go about it, the approach I've tried is to use the given densities and volumes (from the radii) to find the mass of the core and the mantle. Added the masses (it computes to half the Earth's mass ) and then used
g = GM/(R^2).

I'm getting g = 4.1 for part i)

All help would be much appreciated!

Thanks :)
 
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