question_answer 8)

A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at \[{{27.0}^{o}}C\]. What is the change in the diameter of the hole when the sheet is heated to \[{{227}^{o}}C\]? Coefficient of linear expansion of copper\[=2\cdot 2\times {{10}^{9}}N{{m}^{-2}}.\]\[V=1\]

Answer:

In this problem superficial expansion of copper sheet will be involved on heating. Here, area of hole at \[{{10}^{-3}}{{m}^{3}};\] \[\vartriangle V/V=0\cdot 10/100={{10}^{-3}}\] If \[B=\frac{pV}{\vartriangle V}\]cm is the diameter of the hole at \[{{227}^{o}}C\], Then area of the hole at \[{{227}^{o}}C\], \[D=0\cdot 5\]\[=0\cdot 5\times {{10}^{-3}}\] Coefficient of superficial expansion of copper is, \[=5\times {{10}^{-4}}\]\[F=50,000N\] Increase in area =\[5\times {{10}^{-4}}\]or \[P=\frac{F}{\pi {{D}^{2}}/4}=\frac{4F}{\pi {{D}^{2}}}\] \[\therefore \] or \[P=\frac{4\times \left( 5\times {{10}^{4}} \right)}{\left( 22/7 \right)\times {{\left( 5\times {{10}^{-4}} \right)}^{2}}}\]\[{{D}_{2}}=4.2544\,cm\]. Change in diameter \[{{D}_{2}}-{{D}_{1}}=4.2544\,cm-4.24=0.0144\,cm\]