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In an aluminium sheet there is a hole of diameter 1 m and is horizontally mounted on a stand. Onto this hole an iron sphere of diameter 1.004 m is resting. Initial temperature of this system is 25^(@)C. Find at what temperature, the iron sphere will fall down through the hole in sheet. The coefficients of linear expansion for aluminium and iron are 2.4xx10^(-5)and1.2xx10^(-5) respectively.

Answer» <html><body><p></p>Solution :As value of coefficient of linear <a href="https://interviewquestions.tuteehub.com/tag/expansion-980011" style="font-weight:bold;" target="_blank" title="Click to know more about EXPANSION">EXPANSION</a> for aluminium is more thant that for iron, it expands faster than iron. So at some higher temperature when <a href="https://interviewquestions.tuteehub.com/tag/diameter-950836" style="font-weight:bold;" target="_blank" title="Click to know more about DIAMETER">DIAMETER</a> of hole will exactly become <a href="https://interviewquestions.tuteehub.com/tag/equal-446400" style="font-weight:bold;" target="_blank" title="Click to know more about EQUAL">EQUAL</a> to that of iron sphere, the sphere will pass through the hole. Let it happen at some higher temperature T. Thus we have at this temperature T, <br/> `("diameter of hole" )_(Al)` = `("diameterof sphere")_("ion")` <br/> ` 1 [ 1 + alpha_(Al) (T - 25) ] = 1.004 [ 1 + alpha_("iron") ( T - 25) ]` <br/> `alpha_(Al) ( T - 25) = 0.004 + 1.004 alpha_("iron") (T - 25)` <br/> or `T = ((0.004)/(alpha_(A <a href="https://interviewquestions.tuteehub.com/tag/l-535906" style="font-weight:bold;" target="_blank" title="Click to know more about L">L</a>) - 1.004 alpha_("iron")) + 25 ) ""^(@)C ` <br/> or T = `(0.004)/(1 xx 2.4 xx 10^(-<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>) - 1.004 xx 1.2 xx 10^(-5)) + 25 ` <br/> or T = `359.7^(@)` C</body></html>


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