Three liquids of densities $d, 2d$,and $3d$ are mixed in equal volumes. Then the density of the mixture is

$A$ vertical triangular plate $ABC$ is placed inside water with side $BC$ parallel to the water surface as shown. The force on one surface of the plate by water is (density of water is $\rho$ and atmospheric pressure is $P_0$).

Define pressure. Give the $SI$ and $CGS$ unit of pressure.

At every point of a liquid at rest,the tangential stress is zero. Explain with reason.

An open-ended $U$-tube of uniform cross-sectional area contains water (density $1.0 \text{ g/cm}^3$) standing initially $20 \text{ cm}$ from the bottom in each arm. An immiscible liquid of density $4.0 \text{ g/cm}^3$ is added to one arm until a layer $5 \text{ cm}$ high forms,as shown in the figure. What is the ratio $h_2/h_1$ of the heights of the liquid in the two arms?

$A$ vessel with a square cross-section and a height of $6 \ m$ is vertically partitioned. $A$ small window of $100 \ cm^2$ with a hinged door is fitted at a depth of $3 \ m$ in the partition wall. One part of the vessel is filled completely with water and the other side is filled with a liquid having a density of $1.5 \times 10^3 \ kg/m^3$. What force needs to be applied on the hinged door so that it does not open (in $N$)? (Acceleration due to gravity $= 10 \ m/s^2$)