Consider two thermometers $T_1$ and $T_2$ of equal length,which can be used to measure temperature over the range $\theta_1$ to $\theta_2$. $T_1$ contains mercury as the thermometric liquid,while $T_2$ contains bromine. The volumes of the two liquids are the same at the temperature $\theta_1$. The volumetric coefficients of expansion of mercury and bromine are $18 \times 10^{-5} \, K^{-1}$ and $108 \times 10^{-5} \, K^{-1}$,respectively. The increase in length of each liquid is the same for the same increase in temperature. If the diameters of the capillary tubes of the two thermometers are $d_1$ and $d_2$,respectively,then the ratio $d_1: d_2$ is closest to:

• A
  $6.0$
• B
  $2.5$
• C
  $0.6$
• D
  $0.4$