InterviewSolution
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InterviewSolution
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Determine the lengths of an iron rod and copper ruler at `0^@` C if the difference in their lengths at `50^@`C and `450^@`C is the same and is equal to 2 cm. the coefficient of linear expansion of iron`=12xx10^(-6)//K` and that of copper`=17xx10^(-6)//K`. |
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Answer» Let x be the length of the iron rod at `0^@`C y that of the copper rod at `0^@`C, and `Deltal` the difference in lengths at `t_1` and `t_2C^@`. Then `Deltal=x(1+alpha_1t_1)-y(1+alpha_2t_1)` ..(i) and `+-Deltal=x(1+alpha_1t_2)-y(1+alpha_2t_2)` ..(ii) Taking positive sign in equation (ii) `Deltal=x(1+alpha_1t_2)-y(1+alpha_2t_2)` ..(iii) From Eqs. (i) and (iii) we get `xalpha_1=yalpha_2` .(iv) From Eqs. (i) and (iv), we get `y=(lalpha_1)/(alpha_2-alpha_1)=(2xx12xx10^-6)/((17-12)xx10^-6)=4.8cm` and `x=(2xx17xx10^-6)/((17-12)xx10^-6)cm=6.8cm` Taking negative sign in equaiton (ii) `y=(2I+Ialpha_1(t_1+t_2))/((t_2-t_1)(a_2-a_1))`, `x=(2I+Ialpha_2(t_1+t_2))/((t_2-t_1)(alpha_2-alpha_1))` `:. y=(2xx2+2xx12xx10^-6(450+50))/((450-50)(17-12)xx10^-6)cm=2006cm=20.06m` `x=(2xx2+2xx17xx10^-6(450+50))/((450-50)(17-12)xx10^-6)cm=2008.5cm=20.08m` |
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