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In my physics worksheet, a question is given: Q) Cotton and iron of weight 1kg in air are weighed in vacuum. Then-

A)Iron is heavier, B)Cotton is heavier, C)Both weigh 1kg, D)Both have zero weight

I obviously though that in vacuum there is 0 air pressure, so there is no work of air resistance or buoyancy in the question and though the answer is C)Both weigh 1 kg

But the answer is somehow B)Cotton is heavier

I went through a lot of websites, some say it should be C, but some say it should be B),

Can someone please explain me how the answer can be B)?

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    $\begingroup$ I believe this would be a poor exam question. As "weight" can be defined as the force of gravity, but described as the reading on a spring balance, the question is somewhat ambiguous. To add to the problems, cotton may normally contain some water, but would lose some of this in a vacuum, justifying an answer of A. As a worksheet question it is excellent because of the discussion it could generate on these issues. $\endgroup$
    – Peter
    Commented Nov 12, 2023 at 9:17
  • $\begingroup$ To those who voted to close as "homework", note that questions seeking conceptual answers are fine and allowed. This is exactly what this question asks. $\endgroup$
    – StephenG - Help Ukraine
    Commented Nov 12, 2023 at 11:11
  • $\begingroup$ But is the buoyancy bigger than the earths magnetic field on the now magnetized iron? $\endgroup$
    – JEB
    Commented Nov 12, 2023 at 14:50

2 Answers 2

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The answer arises from the establishment of the initial weigh-in procedure, where the the less-dense cotton and the more-dense iron weighed the same, though the cotton displaced more air while being weighed than did the iron.

So, the displaced air that was no longer providing Archimedean partial buoyancy to the cotton, (in the vacuum), constitutes a greater volume than the air similarly formerly doing likewise for the iron, and thus the cotton will show a greater weight.

Regards.

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  • $\begingroup$ I have a question, cant the cotton be compressed to the volume of iron? $\endgroup$
    – randomuser
    Commented Nov 12, 2023 at 8:47
  • $\begingroup$ Not without compressing the atoms themselves, as Carbon atoms are less dense then iron atoms. $\endgroup$
    – sir_khorneflakes
    Commented Nov 12, 2023 at 9:28
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When the cotton is weighed in air, it experieces bouancy (more then the iron). In vaccum, there is no bouyancy. Thus, the "more" on cotton that we had weighed in to correct for bouyancy is now weighed, too.

Please note that this question is confusing if you use the SI system and ist units right. The unit for weight is (strictly speaking) not kg, but Newton. But as we use weight to measure mass, which unit is kg, this is often conflated. And while Mass is conserved, weight isnt.

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  • $\begingroup$ Oh, yes,, I understood the concept, however, if we were to prove it mathematically, how would it be done? $\endgroup$
    – randomuser
    Commented Nov 12, 2023 at 8:28
  • $\begingroup$ Mass is not conserved. Energy is conserved. Mass can be converted to energy and energy can be converted to mass. It is, for example, why the Sun shines (so a rather important distinction for humans). Unfortunately some basic physics and chemistry classes and books still teach than mass is conserved and do not correct that until much later. $\endgroup$
    – StephenG - Help Ukraine
    Commented Nov 12, 2023 at 11:09
  • $\begingroup$ Ya, but at the energy scales of this experiment, mass/energy conversion plays really a neglible role. For a mathematical calculation I would use the inverse density of each material corrected for bouyancy, calculate how much kg I need for one dN and solve that for the desired properties. $\endgroup$
    – sir_khorneflakes
    Commented Nov 13, 2023 at 12:02

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