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 `DeltaT`, the bimetallic strip will bend to form an arc of radius

Options

A. `t//{alpha_(1)+alpha_(2))DeltaT}`
B. `t//{(alpha_(2)-alpha_(1))DeltaT}`
C. `t(alpha_(1)-alpha_(2))DeltaT`
D. `t(alpha_(2)-alpha_(1))DeltaT`

Answer

B

Explanation

Let the angle subtended by the arc formed be `theta`. Then
`theta=(l)/(T) or theta=(Delta l)/(Delta r)=(l_(2)-l_(1))/(r_(1)-r_(2))`
`therefore theta=(l(alpha_(2)-alpha_(1))DeltaT)/(t) or (l)/(r )= (l(alpha_(2)-alpha_(1))DeltaT)/(t)`
So, `r=(t)/((alpha_(2)-alpha_(1))DeltaT)`