Tanks $A$ and $B$ open at the top contain two different liquids up to a certain height. $A$ hole is made in the wall of each tank at a depth $h$ from the surface of the liquid. The area of the hole in $B$ is twice that of in $A$. If the liquid mass flux through each hole is equal, then the ratio of the densities of the liquids respectively, is

$A$ large vessel with a small hole at the bottom is filled with water and kerosene, with kerosene floating on water. The length of the water column is $20 \,cm$ and that of the kerosene is $25 \,cm$. The velocity with which water flows out of the hole is (density of kerosene $= 0.8 \,g/cm^3$, density of water $= 1.0 \,g/cm^3$, neglect viscous force). (in $\,m/s$)

$A$ vessel is filled with water up to a height $h$. When a hole is made at the bottom,all the water drains out in time $t$. If the vessel is filled with water up to a height $4h$,how long will it take for the water to drain out completely when a hole is made at the bottom?

Consider the configuration of a stationary water tank of cross-sectional area $A_{0}$ and a small bucket as shown in the figure below. What is the speed $v$ (in $m/s$) of the bucket so that the water leaking out of a hole of cross-sectional area $A$ (as shown) from the water tank does not fall outside the bucket? (Take $h=5 \, m$,$H=5 \, m$,$g=10 \, m/s^{2}$,$A=5 \, cm^{2}$,and $A_{0}=500 \, cm^{2}$).

$A$ water barrel stands on a table of height $h$. If a small hole is punched in the side of the barrel at its base,it is found that the resultant stream of water strikes the ground at a horizontal distance $R$ from the barrel. The depth of water in the barrel is

$A$ cylindrical vessel filled with water up to a height of $H$ stands on a horizontal plane. The side wall of the vessel has a plugged circular hole touching the bottom. The coefficient of friction between the bottom of the vessel and the plane is $\mu$ and the total mass of the water plus the vessel is $M$. What should be the minimum diameter of the hole so that the vessel begins to move on the floor if the plug is removed? (Here,the density of water is $\rho$)