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.

Explanation

As value of coefficient of linear expansion for aluminium is more thant that for iron, it expands faster than iron. So at some higher temperature when diameter of hole will exactly become equal 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,
`("diameter of hole" )_(Al)` = `("diameterof sphere")_("ion")`
` 1 [ 1 + alpha_(Al) (T - 25) ] = 1.004 [ 1 + alpha_("iron") ( T - 25) ]`
`alpha_(Al) ( T - 25) = 0.004 + 1.004 alpha_("iron") (T - 25)`
or `T = ((0.004)/(alpha_(A l) - 1.004 alpha_("iron")) + 25 ) ""^(@)C `
or T = `(0.004)/(1 xx 2.4 xx 10^(-5) - 1.004 xx 1.2 xx 10^(-5)) + 25 `
or T = `359.7^(@)` C