A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27^(@)C. What is the change in the diameter of the hole when the sheet is heated to 227^(@)C ? (Coefficent of linear expansion of copper = 1.70 xx 10^(-5) ""^(@)C^(-1))

A hole is drilled in a copper sheet. The diameter of the hole is 4.24

1.	A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27^(@)C. What is the change in the diameter of the hole when the sheet is heated to 227^(@)C ? (Coefficent of linear expansion of copper = 1.70 xx 10^(-5) ""^(@)C^(-1))
Answer» `1.44 xx 10^(-2)cm` `1.44 xx 10^(-3) cm` `1.44 xx 10^(-1) cm` `1.44cm` Solution :In this problem superficial expansion of copper SHEET will be involved on heating. Here area of HOLE at `27^(@)C`, `S_(1) = (pi D_(1)^(2))/(4) = (pi)/(4) xx (4.24)^(2) cm^(2)` If `D_(2)` cm is the DIAMETER of the hole at `227^(@)C`, then area of the hole at `227^(@)C`, `S_(2) = (pi D_(2)^(2))/(4) cm^(2)` Coefficient of superficial expansion of copper is `beta= 2 ALPHA = 2 xx 1.70 xx 10^(-5) = 3.4 xx 10^(-5) ""^(@)C^(-1)` Increase in area `=S_(2) - S_(1) = beta S_(1) Delta T` or `S_(2) = S_(1) + beta S_(1) Delta T = S_(1) (1 + beta Delta T)` or `(pi D_(2)^(2))/(4) = (pi)/(4) (4.24)^(2) [1 + 3.4 xx 10^(-5) xx (227-27)]` or `D_(2)^(2) = (4.24)^(2) xx 1.0068 or D_(2) = 4.2544 cm` Change in diameter `=D_(2)-D_(1)= 4.2544-4.24` `=0.0144cm = 1.44 xx 10^(-2)cm`