Three metal rods of the same length and area of cross section form an equilateral triangle as shown in Fig. D is the mid-point of side BC. If AD is independent for small change in temperature, then (${\mathrm{\alpha }}_1$ is the coefficient of linear expansion for rod BC and ${\mathrm{\alpha }}_2$ for rods AB and AC).
 

• A

  ${\mathrm{\alpha }}_1=2{\mathrm{\alpha }}_2$

• B

  ${\mathrm{\alpha }}_1=\frac{{\mathrm{\alpha }}_2}{2}$

• C

  ${\mathrm{\alpha }}_2={\mathrm{\alpha }}_1$

• D

  ${\mathrm{\alpha }}_1=4{\mathrm{\alpha }}_2$