At temperature To, two metal strips of length /o and thickness d is bolted so that their ends coincide. The upper strip is made up of metal A and have coefficient of expansion ${\mathrm{\alpha }}_{\mathrm{A}}$and lower strip is made up of metal B with coefficient of expansion ${\mathrm{\alpha }}_{\mathrm{B}}\left({\mathrm{\alpha }}_{\mathrm{A}}>{\mathrm{\alpha }}_{\mathrm{B}}\right)$. When temperature of their blastic strip is increased from To to $\left({\mathrm{T}}_0+\mathrm{\Delta T}\right)$, one stop becomes longer than the other and the blastic strip is bend in the form of a circle as shown in .
 

The radius of curvature fi of the strip is

• A

  $\mathrm{R}=\frac{\left[2+\left({\mathrm{\alpha }}_{\mathrm{A}}+{\mathrm{\alpha }}_{\mathrm{B}}\right)\mathrm{\Delta T}\right]\mathrm{d}}{2\left({\mathrm{\alpha }}_{\mathrm{A}}-{\mathrm{\alpha }}_{\mathrm{B}}\right)\mathrm{\Delta T}}$

• B

  $\mathrm{R}=\frac{\left[2-\left({\mathrm{\alpha }}_{\mathrm{A}}+{\mathrm{\alpha }}_{\mathrm{B}}\right)\mathrm{\Delta T}\right]\mathrm{d}}{2\left({\mathrm{\alpha }}_{\mathrm{A}}-{\mathrm{\alpha }}_{\mathrm{B}}\right)\mathrm{\Delta T}}$

• C

  $\mathrm{R}=\frac{\left[2+\left({\mathrm{\alpha }}_{\mathrm{A}}-{\mathrm{\alpha }}_{\mathrm{B}}\right)\mathrm{\Delta T}\right]\mathrm{d}}{2\left({\mathrm{\alpha }}_{\mathrm{A}}-{\mathrm{\alpha }}_{\mathrm{B}}\right)\mathrm{\Delta T}}$

• D

  $\mathrm{R}=\frac{\left[2-\left({\mathrm{\alpha }}_{\mathrm{A}}-{\mathrm{\alpha }}_{\mathrm{B}}\right)\mathrm{\Delta T}\right]\mathrm{d}}{2\left({\mathrm{\alpha }}_{\mathrm{A}}-{\mathrm{\alpha }}_{\mathrm{B}}\right)\mathrm{\Delta T}}$