When two metals of equal volume are mixed,the relative density of the mixture is $4$. When equal masses of these two metals are mixed,the relative density of the mixture is $3$. What are the relative densities of the two metals?

$A$ $U$ tube with both ends open to the atmosphere is partially filled with water. Oil,which is immiscible with water,is poured into one side until it stands at a distance of $10\, mm$ above the water level on the other side. Meanwhile,the water rises by $65\, mm$ from its original level (see diagram). The density of the oil is ......... $kg/m^3$.

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

Two communicating vessels contain mercury. The diameter of one vessel is $n$ times larger than the diameter of the other. $A$ column of water of height $h$ is poured into the left vessel. The mercury level will rise in the right-hand vessel ($s =$ relative density of mercury and $\rho =$ density of water) by

Is pressure a scalar or a vector? Give reason.

$A$ nurse measures the blood pressure of a seated patient to be $190 \,mm$ of $Hg$.