Potential Energy of the Atmosphere

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Using the hydrostatic relationship to express density (rho) and height (z) in terms of pressure (p) may not be effective for solving the question. Familiarity with the ideal gas law is suggested as a more useful approach. The discussion emphasizes the importance of providing more context and effort in queries, as per forum guidelines. Participants are encouraged to engage more deeply with the problem rather than simply stating difficulties. Overall, a more thorough understanding of relevant principles is necessary for progress.
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Summary:: I have been trying to do this question for a while using the hydrostatic relationship to put rho and z in terms of p, however, I can not seem to end up with an answer. Can anyone suggest where to start.

The question is as follows:
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Helli @boopdebeep ,
:welcome: ##\qquad# !​
using the hydrostatic relationship to put rho and z in terms of p
might not be so useful. Do you know about the ideal gas law ?

btw: PF rules ask a bit more from you than just 'can't find an answer' ... :frown:

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Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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