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A Sphere A is placed on a smooth table.Another sphere B is suspended as shown in the figure.Both the spheres are identical in all respects.Equal quantity of heat is supplied to both spheres.All kinds of heat loss are neglected.The final temperatures of A & B are T1 & T2 respectively,then

  • T1>T2
  • T1 = T2
  • T1
  • None of these

Please give reasons for your answer.

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closed as off topic by David Z Jul 29 '11 at 5:32

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3  
Looks like this question was already asked on Yahoo! Answers. Here is the question: answers.yahoo.com/question/… –  Bernhard Heijstek Jul 28 '11 at 7:55
    
Peter Coles posted a version of this question on his blog not too long ago, and it led to much discussion (partly because many people, including me, didn't quite understand the question as he phrased it). telescoper.wordpress.com/2011/05/17/cute-physics-problem –  Ted Bunn Jul 28 '11 at 13:54
    
This is actually a pretty interesting question, but I think I have to close it under the same reasoning I described on your other question. We expect questions to have some thought put into them. In particular, I'd point you to this meta question which gives some guidelines on how to ask these sorts of questions. –  David Z Jul 29 '11 at 5:34
    
@David I think you are taking a really hard stand here. This is a really interesting question and should belong to the Physics.SE. Of course the way it was asked may not meet the guidelines of the site. But closing it right away would scare people off from the site. Maybe you could give a warning and wait for the person to edit the question and rephrase it in such a way that it suits the site. –  Bernhard Heijstek Jul 30 '11 at 9:35
    
@Bernhard: in that sense, closing is a warning. Generally, when I close a question I leave a comment indicating how the poster can edit it to make it acceptable. –  David Z Jul 30 '11 at 10:33

1 Answer 1

up vote 2 down vote accepted

This is an old physics olympiad problem, I think. The answer hinges on the spheres expanding due to heating. Sphere A raises its center of mass some and sphere B lowers its center of mass some. By conservation of energy sphere A is thus slightly colder, since more of its energy went into its gravitational potential.

It's a bit of a silly problem since the effect is extremely small. We can see this because from common experience if you heat a metal sphere $10 C$, the change in radius is pretty small - so small you probably won't notice without measuring it or else having something with a different expansion coefficient wrapped around the sphere. Meanwhile, if you drop a fist-sized a metal sphere by $1cm$, a distance much larger than such a sphere would expand with a $10 C$ change, the temperature change is much, much smaller than $10 C$. It's smaller than you can even notice, really. So the gravitational potential change is very small compared to the heat, and the difference in temperatures is minute.

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I agree that the problem is a bit silly. And the problem formulation (v4) does not exclude a material with negative thermal expansion, which would lead to the opposite conclusion en.wikipedia.org/wiki/Negative_thermal_expansion –  Qmechanic Jul 28 '11 at 9:59

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