Two straight metallic strips each of thickness t and length...

Two straight metallic strips each of thickness $t$ and length $L$ are rivetted together. Their coefficients of linear expansions are $\alpha_{1}$ and $\alpha_{2} .$ If they are heated through temperature $\Delta \theta$, the bimetallic strip will bend to form an arc of radius (a) $t /\left[\left(\alpha_{1}+\alpha_{2}\right) \Delta T\right]$ (b) $t /\left[\left(\alpha_{2}-\alpha_{1}\right) \Delta T\right]$ (c) $t\left(\alpha_{1}+\alpha_{2}\right) \Delta T$ (d) $t\left(\alpha_{2}-\alpha_{2}\right) \Delta T$

Two straight metallic strips each of thickness $t$ and length $L$ are rivetted together. Their coefficients of linear expansions are $\alpha_{1}$ and $\alpha_{2} .$ If they are heated through temperature $\Delta \theta$, the bimetallic strip will bend to form an arc of radius
(a) $t /\left[\left(\alpha_{1}+\alpha_{2}\right) \Delta T\right]$
(b) $t /\left[\left(\alpha_{2}-\alpha_{1}\right) \Delta T\right]$
(c) $t\left(\alpha_{1}+\alpha_{2}\right) \Delta T$
(d) $t\left(\alpha_{2}-\alpha_{2}\right) \Delta T$

Key Concepts

Bimetallic Strip

A bimetallic strip is a composite structure consisting of two bonded metals with different coefficients of thermal expansion. When heated, the mismatch in expansion between the two metals causes the strip to bend, making bimetallic strips useful in temperature sensing and actuation applications. Their behavior is a practical example of differential thermal expansion.

Radius of Curvature

The radius of curvature is a measure of how sharply a curved object bends, representing the radius of the circle that best approximates the curve at a given segment. In the context of a bimetallic strip, the radius of curvature is determined by the difference in thermal expansions and the thickness of the strip, establishing a relationship between material properties, temperature change, and the resulting curvature.

Thermal Expansion

Thermal expansion refers to the tendency of materials to change their dimensions in response to changes in temperature. This is quantified by the coefficient of linear expansion, which measures the fractional change in length per unit temperature change. Understanding thermal expansion is crucial in predicting how materials behave under varying thermal conditions.

Differential Thermal Expansion

Differential thermal expansion occurs when two different materials, each with its own coefficient of linear expansion, expand by different amounts when subjected to a temperature change. This difference in expansion can lead to internal stresses or deformations, such as bending in composite structures, as one material expands more than the other.

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