A) Proportional to DT
B) Inversely proportional to DT
C) Proportional to \[|{{\alpha }_{B}}-{{\alpha }_{C}}|\]
D) Inversely proportional to \[|{{\alpha }_{B}}-{{\alpha }_{C}}|\]
Correct Answer: D
Solution :
Let L0 be the initial length of each strip before heating. Length after heating will be \[{{L}_{B}}={{L}_{0}}(1+{{\alpha }_{B}}\Delta T)=(R+d)\theta \] \[{{L}_{C}}={{L}_{0}}(1+{{\alpha }_{C}}\Delta T)=R\theta \] Þ \[\frac{R+d}{R}=\frac{1+{{\alpha }_{B}}\Delta T}{1+{{\alpha }_{C}}\Delta T}\] Þ \[1+\frac{d}{R}=1+({{\alpha }_{B}}-{{\alpha }_{C}})\Delta T\] Þ \[R=\frac{d}{({{\alpha }_{B}}-{{\alpha }_{C}})\Delta T}\] Þ \[R\propto \frac{1}{\Delta T}\] and \[R\propto \frac{1}{({{\alpha }_{B}}-{{\alpha }_{C}})}\]You need to login to perform this action.
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