Diagram shows a jar filled with two non mixing liquids $1$ and $2$ having densities ${\rho _1}$ and ${\rho _2}$ respectively. A solid ball, made of a material of density ${\rho _3}$ , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ${\rho _1}$ , ${\rho _2}$ and ${\rho _3}$ ?
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A cylinder containing water up to a height of $25 cm$ has a hole of cross-section $\frac{1}{4}c{m^2}$ in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out
According to Bernoulli's equation $\frac{P}{{\rho g}} + h + \frac{1}{2}\,\frac{{{v^2}}}{g} = {\rm{constant}}$ The terms $A, B$ and $ C$ are generally called respectively:
The pressure at the bottom of a water tank is $4 P$. where $P$ is atmospheric pressure. If water is drawn out till the water level decreases by $\frac{3}{5}$ th, then pressure at the bottom of the tank is .........
Under a constant pressure head, the rate of flow of liquid through a capillary tube is $V$. If the length of the capillary is doubled and the diameter of the bore is halved, the rate of flow would become
A liquid flows through a horizontal tube. The velocities of the liquid in the two sections, which have areas of cross-section ${A_1}$ and ${A_2}$, are ${v_1}$ and ${v_2}$ respectively. The difference in the levels of the liquid in the two vertical tubes is $ h$
A liquid flows in a tube from left to right as shown in figure. ${A_1}$ and ${A_2}$ are the cross-sections of the portions of the tube as shown. Then the ratio of speeds ${v_1}/{v_2}$ will be
Two copper vessels $A$ and $B$ have the same base area but of different shapes. $A$ takes twice the volume of water as that $B$ requires to fill upto a particular common height. Then the correct statement among the following is
A particle released from rest is falling through a thick fluid under gravity. The fluid exerts a resistive force on the particle proportional to the square of its speed. Which one of the following graphs best depicts the variation of its speed $v$ with time $t$ ?
A spherical body of radius $R$ consists of a fluid of constant density and is in equilibrium under its own gravity. If $P ( r )$ is the pressure at $r ( r < R )$, then the correct option$(s)$ is(are)
$(A)$ $P ( I =0)=0$ $(B)$ $\frac{ P ( r =3 R / 4)}{ P ( r =2 R / 3)}=\frac{63}{80}$
$(C)$ $\frac{ P ( r =3 R / 5)}{ P ( r =2 R / 5)}=\frac{16}{21}$ $(D)$ $\frac{ P ( r = R / 2)}{ P ( r = R / 3)}=\frac{20}{27}$
Water enters through end $A$ with speed ${v_1}$ and leaves through end $B$ with speed ${v_2}$ of a cylindrical tube $AB$. The tube is always completely filled with water. In case $I$ tube is horizontal and in case $ II$ it is vertical with end $ A $ upwards and in case $ III $ it is vertical with end $B$ upwards. We have ${v_1} = {v_2}$ for