# Heat on rod!

**Classical Mechanics**Level 3

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 \(\Delta t\), 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),

Type 2 for option (b),

Type 3 for option (c),

Type 4 for option (d).