$5 \text{ litres}$ of benzene weighs

$A$ 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 $P_0$).

$A$ thin uniform tube is bent into a circle of radius $r$ in the vertical plane. Equal volumes of two immiscible liquids,whose densities are ${\rho _1}$ and ${\rho _2}$ $({\rho _1} > {\rho _2})$,fill half the circle. The angle $\theta$ between the radius vector passing through the common interface and the vertical is

In making an alloy,a substance of specific gravity $s_1$ and mass $m_1$ is mixed with another substance of specific gravity $s_2$ and mass $m_2$; then the specific gravity of the alloy is

$A$ 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 $= 10 \ m/s^2$)

Equal masses of water and a liquid of density $2 \ g/cm^3$ are mixed together. The density of the resulting mixture is ........ $g/cm^3$.