$A$ square gate of size $1\,m \times 1\,m$ is hinged at its mid-point. $A$ fluid of density $\rho$ fills the space to the left of the gate. The force $F$ required to hold the gate stationary is

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

In the arrangement shown, both the vessels $A$ and $B$ are identical, but the amount of water in $B$ is double that in $A$. The vessels are closed by identical leak-proof pistons at the same height. The pistons are connected to the ends of a lever arm. There is no friction between the pistons and the container walls. The system is in equilibrium in the situation shown. Now, the valve in the horizontal tube connecting both the vessels is opened. In which direction will the water flow through the tube?

The pressure of confined air is $p$. If the atmospheric pressure is $P$,then

$A$ siphon in use is demonstrated in the following figure. The density of the liquid flowing in the siphon is $1.5 \text{ g/cm}^3$. The pressure difference between the points $P$ and $S$ will be

Define density. Write its unit and dimensional formula.