A bimetallic strip is formed out of two identical strips one of copper and the other of brass. The coefficients of linear expansion of the strip goes up by `DeltaT`and the strip bends to from an arc of radius of curvature R. Then R is.

Options

A. proportional to `DeltaT`
B. inversely proportional to `DeltaT`
C. proportional to `|alpha_B-alpha_C|`
D. inversely proportional to `|alpha_B-alpha_C|`

Answer

B, D

Explanation

(b,d)
Co-efficient of linear expansion of brass is greater than that
of copper i.e., `alpha_Bgtalpha_C.` Now,
`L_B=L_0(1+alpha_BDeltaT)`
or, `(R+d)theta=L_0(1+alpha_BDeltaT)`
Again, `L_C=L_0(1+alpha_CDeltaT)`
or, `R theta=L_0(1+alpha_CDeltaT)`
`:. ((R+d) theta) /(R theta)=(1+alpha_BDeltaT)/(1+alpha_CDeltaT)`
or, `(R+d)/R=(1+alpha_BDeltaT)(1+alpha_CDeltaT), by binomial
theoram.
or `1+d/R=1+(alpha_B-alpha_C)DeltaT-alpha_B alpha_C(DeltaT)^2`
or, `d/R=(alpha_B-alpha_C) DeltaT or R=d/((alpha_B-alpha_C)DeltaT)`
`:. Rprop1/(DeltaT) and Rprop1/|alpha_B-alpha_C|