KVPY SX SB Exam 20141 Question Paper

Consider two thermometers T ${}_1$ and T${}_2$ of equal length which can be used to measure temperature over the range ${\mathit{\theta }}_1\mathrm{to}{\mathit{\theta }}_{2.}$ 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 ${\mathit{\theta }}_1$. The volumetric coefficients of expansion of mercury and bromine are $18\times {10}^{-5}{\mathit{K}}^{-1}$ and$108\times {10}^{-5}{\mathit{K}}^{-1}$ , respectively. The increase in length of each liquid is the same for the same increase in temperature. Ifthe diameters of the capillary tubes of the two thermometers are ${\mathit{d}}_1$ and ${\mathit{d}}_2$ respectively, then the ratio ${\mathit{d}}_1:{\mathit{d}}_2$ would be closest to