Two substances of densities ${\rho _1}$ and ${\rho _2}$ are mixed in equal volumes and the relative density of the mixture is $4$. When they are mixed in equal masses,the relative density of the mixture is $3$. The values of ${\rho _1}$ and ${\rho _2}$ are

If a vessel containing a fluid of density $\rho$ up to height $h$ is accelerated vertically downwards with acceleration $a_0$,then the pressure by the fluid at the bottom of the vessel is given by the equation ........ ($p_0$ denotes the atmospheric pressure and $g$ denotes the acceleration due to gravity).

Select the wrong statement about pressure.

Give the names of physical quantities which are needed to describe a fluid.

$A$ cubical block of wood, of length $10 \,cm$, floats at the interface between oil of density $800 \,kg/m^3$ and water. The lower surface of the block is $1.5 \,cm$ below the interface. If the depth of water is $10 \,cm$ below the interface and oil is up to $10 \,cm$ above the interface, then the difference in pressure at the lower and the upper face of the wooden block is:
(Assume density of water, $\rho_w = 1000 \,kg/m^3$ and acceleration due to gravity, $g = 10 \,m/s^2$) (in $\,Pa$)

Two points $A$ and $B$ are at the same depth in a liquid at rest. Then the pressure on them $P_A$ ........... $P_B$.