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 xx 10^(-5) K^(-1) " and " 108 xx 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)` would be closest to

Options

A. 6
B. 2.5
C. 0.5
D. 0.4

Answer

D

Explanation

Increase in length of each liquid is same
`Delta l_1=Delta l_2`
`implies (DeltaV_(Hg))/(Delta d_1^2)=(DeltaV_("Bromine"))/(Delta d_2^2)`
`implies (d_1)/(d_2)=sqrt(1/6)=0.4`