[net.puzzle] Expansion of a hole in a sphere etc.

mvramakrishn@watdaisy.UUCP (Rama) (10/28/85)

	I do not have the complete answer but I think I can point out
	the right direction of thinking.

	Consider a thin ring: no body questions that the hole expands.

	But in case of a disc with a small hole in it, what happens is 
	not straightforward.
	If you consider disc as made up of a number of concentric rings (thin)
	each ring expands by same proportion and hence the whole disc
	expands including the hole.
	If you partition the disc into wedge shaped strips, when heated
	each strip expands. Then it seems that the hole should shrink in
	size while the overall disc expands.
	The combination of the above two views explains what happens exactly.

	When the disc is heated stresses are induced because of expansion.
	Whether the hole expands or shrinks is dependent on the
	Ratio of the diameter of the disc to that of the hole,
	the coeff of expansion, the coeff of elasticity etc.
	I think some Civil Engr./Strength of materials people should
	be able to give exact answers. (may be this is an old problem for them).

...Rama...