Gauss's law states that f 9.dA= −47GM. A spherical star of mass M and radius R has a uniform density. By applying Gauss's law to a suitable Gaussian surface, show that the magnitude of g within the star rises linearly with radius r. In practice, a star is likely to have a higher density near its center. By referring to Gauss's law, explain in outline what effect this would have on g at a given radius r. Sketch g as a function of r for the above two situations (for r < R and assuming that in both cases the star has the same total mass M).

Gauss's law states that f 9.dA= −47GM. A spherical star of mass M and radius R has a uniform density. By applying Gauss's law to a suitable Gaussian surface, show that the magnitude of g within the star rises linearly with radius r. In practice, a star is likely to have a higher density near its center. By referring to Gauss's law, explain in outline what effect this would have on g at a given radius r. Sketch g as a function of r for the above two situations (for r < R and assuming that in both cases the star has the same total mass M).

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Gauss's law states that
fg.dA= -4RGM.
A spherical star of mass M and radius R has a uniform density. By applying Gauss's law to
a suitable Gaussian surface, show that the magnitude of g within the star rises linearly with
radius r.
In practice, a star is likely to have a higher density near its center. By referring to Gauss's law,
explain in outline what effect this would have on g at a given radius r.
Sketch g as a function of r for the above two situations (for r < R and assuming that in both
cases the star has the same total mass M).

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Step 2: Draw a spherical element inside a sphere:

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Step 3: a) Calculate the magnitude of g within the star with uniform density:

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Step 4: b) Calculate the magnitude of g within the star with varying density:

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Step 5: Draw the graphs:

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