Question

$A$ $U$ tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are at the same level with $10cm$ of water in one arm and $12.5cm$ of spirit in the other as shown in figure. The relative density of the spirit is

• A. $0.6$
• B. $0.8$
• C. $1.0$
• D. $1.25$

Answer 1

Answer: (B)

Refer figure
As the mercury columns in the two arms of $U$ tube are at the same level, therefore

Pressure due to water = Pressure due to spirit column
${\rho }_w{h}_{w}g={\rho }_s{h}_{s}g$
${\rho }_s=\frac{h_w}{h_s}{\rho }_w$
$\therefore$ Relative density of spirit $=\frac{{\rho }_s}{{\rho }_w}=\frac{h_w}{h_s}=\frac{10cm}{12.5cm}=0.8$