An open $U$-tube contains mercury. When $11.2 \,cm$ of water is poured into one of the arms of the tube, how high does the mercury rise in the other arm from its initial level (in $\,cm$)?

Three liquids of equal masses are taken in three identical cubical vessels $A$,$B$,and $C$. Their densities are $\rho_{A}$,$\rho_{B}$,and $\rho_{C}$ respectively,where $\rho_{A} < \rho_{B} < \rho_{C}$. The force exerted by the liquid on the base of the cubical vessel is

$A$ cylinder stands vertically in two immiscible liquids of densities $\rho$ and $2\rho$. The heights of the two liquids are shown in the figure. Find the difference in pressure at point $A$ and point $B$.

Three liquids of densities $d$,$2d$,and $3d$ are mixed in equal proportions of weights. The relative density of the mixture is

Fill in the blanks:
$(i)$ $1 \text{ atm} = \dots \text{ Pascal}$
$(ii)$ $1 \text{ torr} = \dots \text{ Pascal}$
$(iii)$ $1 \text{ bar} = \dots \text{ Pa}$
$(iv)$ $1 \text{ atm} = \dots \text{ cm Hg}$

$A$ $U$-tube containing a liquid moves with a horizontal acceleration $a$ along a direction joining the two vertical limbs. The separation between these limbs is $d$. The difference in their liquid levels is