A hole is drilled in a metal sheet. At 27^{ci | vedclass

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Question

(A) Let the initial diameter be $d_0 = 5\,cm$ at temperature $T_1 = 27^{\circ}C$.When the sheet is heated to $T_2 = 177^{\circ}C$,the change in temper

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(A) Let the initial diameter be $d_0 = 5\,cm$ at temperature $T_1 = 27^{\circ}C$.When the sheet is heated to $T_2 = 177^{\circ}C$,the change in temperature is $\Delta T = T_2 - T_1 = 177^{\circ}C - 27^{\circ}C = 150^{\circ}C$.The change in diameter $\Delta d$ is given by the formula for linear expansion: $\Delta d = d_0 \alpha \Delta T$.Substituting the given values: $\Delta d = 5\,cm 	imes (1.6 	imes 10^{-5} /^{\circ}C) 	imes 150^{\circ}C$.$\Delta d = 5 	imes 1.6 	imes 150 	imes 10^{-5}\,cm$.$\Delta d = 1200 	imes 10^{-5}\,cm = 12 	imes 10^{-3}\,cm$.Comparing this with $d 	imes 10^{-3}\,cm$,we get $d = 12$.

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