Question

A vertical uniform $U$ tube open at both ends contains mercury. Water is poured in one limb until the level of mercury is depressed $2cm$ in that limb. The length of water column when this happens in cm (rounded off to nearest integer).

Answer 1

if level of mercury is depressed $2cm$ in one limb, then total difference in height of mercury columns is $4cm$. so pressure by $4cm$ of mercury column is provided by $x$ cm of water. so we have
$h_m{\rho }_{m}g=h_w{\rho }_{w}g\Rightarrow 4\times 13594=x\times 1000\Rightarrow x=54.376cm\approx 54.4cm$