Question

A $U$ tube with both ends open to atmosphere is partially filled with water reaching a mark of $45mm$. An immiscible liquid is poured into one side until it stands at a distance of $5mm$ above the water level on the other side. Meanwhile water level rises by $40mm$ from its original level. Density of liquid is________ $kg/m^3$.

Answer 1

Answer: 944.44

The system is in equilibrium and pressure on both sides is equal.
This means, $h_w{\rho }_{w}g=h_0{\rho }_{0}g$
$\therefore {\rho }_0=\frac{h_w{\rho }_w}{h_0}=\frac{85\times 10^{-3}\times 10^3}{90\times 10^{-3}}$
$=\frac{17}{18}\times 10^3$
$\therefore {\rho }_0=944.44kg/m^3$ ....(Rounding off to $2$ decimal places)