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 $10\, cm$ of water in one arm and $12.5\, cm$ 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 $=\frac{\rho_{s}}{\rho_{w}}=\frac{h_{w}}{h_{s}}=\frac{10 \,cm}{12.5 \,cm}=0.8$