The question: A steel rod is 3.000 cm in diameter at 19.00°C. A brass ringhas an

Question

The question:

A steel rod is 3.000 cm in diameter at 19.00°C. A brass ringhas an interior diameter of 2.991 cm at 19.00°C. At what common temperature will thering just slide onto the rod?

I understand how to solve this problem, I would just like to knowwhy do the diameters of both the steel rod and the brass ring haveto be equal? To me, it seems that the rod would be the innerdiameter and the brass ring the outer, thus the ring should beslightly larger in diameter to the rod. I would greatly appreciatean explanation why my intuition wouldn't be the case. That's all.No solving anything.

Thanks in advance!

Explanation / Answer

.       *   Thesteel rod is a solid bar without any hollow portion inside. Hence,it has only             onediameter i.e., outer diameter. .       *   Thebrass ring is hollow in the middle. Hence, it posess both inner andouter
           diameters. .       *   Thecondition to fit the rod into the ring is outer diameter of thesteel rod is equal           tothe inner diameter of the ring. .       *   Initially,the inner diameter of the ring ( 2.991 cm ) is smaller than theouter
         diameter of the steel rod ( 3.000 cm ).Hence, ring cannot be inserted into the rod. .       *   Whenboth of them are heated simultaneously, then brass expands norethan
           steelbecause it has more linear coefficientof expansion. .       *   At onecommon temperature, inner diameter of the ring becomes same asthat
          ofouter diameter of the steel rod so that brassring can be inserted into the rod.

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