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Will it grow or shrink?

Few days back I encountered this problem on brilliant. But I am not satisfied with the explanation given there and the answer as well. I discussed with many of my friends and also few faculty members in my institute but even they are confused and not sure. Can we discuss it and find the right answer? I hope that David, Peter and Calvin will also take part in the discussion.

Thank you

Note by Snehal Shekatkar
3 years, 5 months ago

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I hope this explanation can satisfy you @Snehal Shekatkar . Note that, if you satisfy with the answer, please immediately delete this note to ensure the secrecy of that good problem.


Repost from : Physics Stack Exchange

Instead of a circular hole, let's think of a square hole. You can get a square hole two ways, you can cut it out of a complete sheet, or you can get one by cutting a sheet into 9 little squares and throwing away the center one. Since the 8 outer squares all get bigger when heat it, the inner square (the hole) also has to get bigger:

enter image description here

enter image description here

Same thing happens with a round hole.


This is confusing to people because the primary experience they have with stuff getting larger when heated is by cooking. If you leave a hole in the middle of a cookie and cook it, yes, the cookie gets bigger and the hole gets smaller. But the reason for this is that the cookie isn't so solid. It's more like a liquid, it's deforming. And as Ilmari Karonen points out, the cookie sheet isn't expanding much so there are frictional forces at work.


Credit answer : Carl Brannen

Carl Brannen

Carl Brannen

Tunk-Fey Ariawan · 3 years, 5 months ago

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@Tunk-Fey Ariawan plz also see https://brilliant.org/discussions/thread/are-events-predefined/ Nishant Sharma · 3 years, 5 months ago

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Consider a circular ring which is very thin if you heat this ring the area inside the ring will surely increase as the ring will try to keep its shape the same but increase in length so the only way to do so is by increasing the radius of the circle. The metal around the hole can be now replaced by many such rings. Harsh Depal · 3 years, 5 months ago

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@Harsh Depal Yeah I agree. Mardokay Mosazghi · 3 years, 5 months ago

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@Harsh Depal But harsh, we know that when we heat metal, it expands where it gets space. So, the ring in the center should decrease as the disk expands... Abhineet Nayyar · 3 years, 5 months ago

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Mr.@Tunk-Fey Ariawan there is no good in withholding knowledge. Share it. It doesn't cost you. Suresh Kumar · 3 years, 5 months ago

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@Suresh Kumar Just call me Ari, please. Without Mr. :)

It's not about withholding knowledge Suresh, but merely to respect the problem creator. If this note is not the part of the member's problem, I'll be glad to share it. Tunk-Fey Ariawan · 3 years, 5 months ago

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@Tunk-Fey Ariawan also veiw https://brilliant.org/discussions/thread/are-events-predefined/ plz Nishant Sharma · 3 years, 5 months ago

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@Tunk-Fey Ariawan Any how Ari, the explanation you submitted(May not be yours) was very apt. Suresh Kumar · 3 years, 5 months ago

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it has to expand, or else the nut, which would also expand, would suffer from heavy compression Mrinmay Dhar · 3 years, 5 months ago

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This is physics, right? So why don't we just experiment? Patrick Engelmann · 3 years, 5 months ago

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also discuss on https://brilliant.org/discussions/thread/are-events-predefined/ Nishant Sharma · 3 years, 5 months ago

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why don't we try using a meshing software like ansys. The animation of result will explain us clear Suresh Kumar · 3 years, 5 months ago

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I too have the same problem, Snehal...thnx for opening the discussion... :) Abhineet Nayyar · 3 years, 5 months ago

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