Heat on rod!

Two straight metallic strips each of thickness \(t\) and length \(l\) are riveted together. Their coefficients of linear expansion are \(\alpha_1 \) and \(\alpha_2\). If they are heated through a temperature of \(\Delta t\), the bimetallic strip will bend to form an arc of radius \(r.\)

Find \(r.\)

• (a) \(\ \dfrac t{(\alpha_1 + \alpha_2) \Delta t} \)
• (b) \(\ \dfrac t{(\alpha_2-\alpha_1) \Delta t} \)
• (c) \(\ {(\alpha_1+\alpha_2) \Delta t} \)
• (d) \(\ {(\alpha_2-\alpha_1) \Delta t} \)

Type 1 for option (a), 2 for option (b), 3 for option (c), or 4 for option (d).