Question

Temperature of a bimetallic strip of copper and zinc rivetted together is increased from ${20}^{\circ }\text{C}$ to ${100}^{\circ }\text{C}$. Which of the following options correctly represents the final condition of the bimetallic strip?
$[Z{n}_{\alpha }=30\times {10}^{-6}/{}^{\circ }C,C{u}_{\alpha }=17\times {10}^{-6}/{}^{\circ }C]$

• A. Zinc strip will be on outer side of arc.
• B. Copper strip will be on outer side of arc.
• C. Bimetal will not bend.
• D. Data insufficient

Answer 1

The correct option is A Zinc strip will be on outer side of arc.

Since the the strips are rivetted together, they cannot move along each other due to expansion. Hence they will bend.
$L_{\circ }=20\text{cm}$
$\Delta T={80}^{\circ }\text{C}$
${\alpha }_{Zn}=30\times {10}^{-6}/{}^{\circ }\text{C}$
${\alpha }_{Cu}=17\times {10}^{-6}/{}^{\circ }\text{C}$
We know for linear expansion, length of strip
$L=L_{\circ }(1+\alpha \Delta T)$
For Zn,
$L_{Zn}=20(1+30\times {10}^{-6}\times 80)=20.048\text{cm}$
For Cu,
$L_{Cu}=20(1+17\times {10}^{-6}\times 80)$$=20.027\text{cm}$
As, $L_{Zn}>L_{Cu}$


Therefore, zinc strip will be on outer side as length of outer arc is greater.