A steady flow of a liquid of density $\rho$ is shown in figure. At point $1$, the area of crosssection is $2A$ and the speed of flow of liquid is $\sqrt{2} \mathrm{m} {\mathrm{s}}^{-1}$. At point $2$, the area of crosssection is $A$. Between the points $1$ and $2$, the pressure difference is $100 \mathrm{N} {\mathrm{m}}^{-2}$ and the height difference is $10 \mathrm{cm}$. The value of $\rho$ is
(Acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A cylindrical container containing water has a small hole at height of $H=8 \mathrm{cm}$ from the bottom and at a depth of $2 \mathrm{cm}$ from the top surface of the liquid. The maximum horizontal distance travelled by the water before it hits the ground $\left(x\right)$ is

Consider a water tank as shown in the figure. It's cross-sectional area is $0.4{ \mathrm{m}}^2$. The tank has an opening $B$ near the bottom whose cross-section area is $1{ \mathrm{cm}}^2$. A load of $24 \mathrm{kg}$ is applied on the water at the top when the height of the water level is $40 \mathrm{cm}$ above the bottom, the velocity of water coming out the opening $B$ is $\mathrm{v} \mathrm{m} {\mathrm{s}}^{-1}$. The value of $v$, to the nearest integer, is ___ .[Take the value of $g$ to be $10{ \mathrm{m} \mathrm{s}}^{-2}$]

In the diagram shown, the difference in the two tubes of the manometer is $5 \mathrm{cm}$, the cross-section of the tube at $A$ and $B$ is $6 {\mathrm{mm}}^2$ and $10 {\mathrm{mm}}^2$ respectively. The rate at which water flows through the tube is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A light cylindrical vessel is kept on a horizontal surface. Area of the base is $A.$ A hole of cross-sectional area $a$ is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is