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A U tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with $10.0 \mathrm{~cm}$ of water in one arm and $12.5 \mathrm{~cm}$ of spirit in the other, what is the relative density of spirit?
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For water column in one arm of $U$ tube, $\mathrm{h}_1=10.0 \mathrm{~cm} ; \rho_1($ density $)=1 \mathrm{~g} \mathrm{~cm}^{-3}$
For the spirit column in the other arm of $\mathrm{U}$ tube, $\mathrm{h}_2=12.5$ $\mathrm{cm} ; \rho_2=$ ?
As the mercury columns in the two arms of $U$ tube are in level,
$\therefore$ pressure exerted by each is equal.
Hence, $h_1 \rho_1 g=h_2 \rho_2 g$
or $\mathrm{P}_2=\frac{\mathrm{h}_1 \rho_1}{\mathrm{~h}_2}=\frac{10 \times 1}{12.5}=0.8 \mathrm{~g} \mathrm{~cm}^{-3}$
$\therefore \quad$ Relative density of spirit $=\frac{\rho_2}{\rho_1}=\frac{0.8}{1}$
For the spirit column in the other arm of $\mathrm{U}$ tube, $\mathrm{h}_2=12.5$ $\mathrm{cm} ; \rho_2=$ ?
As the mercury columns in the two arms of $U$ tube are in level,
$\therefore$ pressure exerted by each is equal.
Hence, $h_1 \rho_1 g=h_2 \rho_2 g$
or $\mathrm{P}_2=\frac{\mathrm{h}_1 \rho_1}{\mathrm{~h}_2}=\frac{10 \times 1}{12.5}=0.8 \mathrm{~g} \mathrm{~cm}^{-3}$
$\therefore \quad$ Relative density of spirit $=\frac{\rho_2}{\rho_1}=\frac{0.8}{1}$
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