Pascal's Law

A U-tube having a horizontal arm of length $20 \mathrm{cm}$, has a uniform cross-sectional area $1 {\mathrm{cm}}^2$. It is filled with water of volume $60 \mathrm{cc}$. The volume of a liquid of density $4 \mathrm{g} {\mathrm{cc}}^{-1}$ required to be poured in one arm of the U-tube so that no water is left in the horizontal arm of the tube is (take $\mathrm{g}=9.8 \mathrm{m} {\mathrm{s}}^{-2}$)

A vertical uniform U tube open at both ends contains mercury. Water is poured in one limb until the level of mercury is depressed 2cm in that limb. What is the length of water column when this happens.

Given below are two statements:

Statement I: Pressure in a reservoir of water is same at all points at the same level of water.

Statement II: The pressure applied to enclosed water is transmitted in all directions equally.

In the light of the above statements, choose the correct answer from the options given below:

A liquid of density$\rho$ is filled in a vessel of cross-sectional area $A$upto height$h$. A block of mass $M$and cross-sectional area$a$ is made to float in it as shown in figure. The pressure at the bottom of the vessel will be

An open U-tube contains mercury. When $13.6 \mathrm{cm}$ of water is poured into one of the arms of the tube then the mercury rise in the other arm from its initial level is

The tank shown in figure is filled with water upto a height of $2 \mathrm{m}$. Assuming the atmospheric pressure to be absent the force that the water exerts on force $ABCD$ is equal to ($g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$ and density of water = $1000 \mathrm{kg} {\mathrm{m}}^{-3}$)

The side of glass aquarium is $1 \mathrm{m}$ high and $2 \mathrm{m}$ long. When the aquarium is filled to the top with water, what is the total force against the side-

In rising from the bottom of a lake to top, the temperature of an air bubble remains unchanged but its diameter gets tripled. If h is barometric height expressed in meter of mercury of relative density$\rho$, at the surface of lake, depth of lake in
meter is
 

There are four cylindrical vessels identical in dimensions. If these are filled with equal masses of four different liquids P, Q, R, and S such that their densities are ${\mathrm{\rho }}_{\mathrm{P}}>{\mathrm{\rho }}_{\mathrm{R}}>{\mathrm{\rho }}_{\mathrm{S}}$, then pressure at the base of vessels is 

Which of the following is correct?

The increasing order of normal reaction applied by the base of vessels on the liquid are (Given base area $A_A<A_B<A_C$)

For a liquid contained in a container, pressure $\left(P\right)$ versus the depth of liquid coloumn $\left(h\right)$ a graph is shown below by the solid line. If $\rho$ is density of liquid and $\tan \alpha =\rho g$) then choose the correct alternative?

A long container has a square base of side $L$ . The height to which water should be filled so that the force on one of its side surface is the same as that at its bottom is (ignore atmospheric pressure)

A U-tube having a horizontal arm of length $20 \mathrm{cm}$, has a uniform cross-sectional area $1 {\mathrm{cm}}^2$. It is filled with water of volume $60 \mathrm{cc}$. The volume of a liquid of density $4 \mathrm{g} {\mathrm{cc}}^{-1}$ required to be poured in one arm of the U-tube so that no water is left in the horizontal arm of the tube is (take $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$)

A liquid of density $\rho$ is filled in a U-tube is accelerated with an acceleration $a$ so that the height of liquid in its two vertical arms are $h_1$ and$h_2$ as shown in the figure. If $l$ is the length of horizontal arm of the tube, the acceleration $a$ is

There is a circular tube in a vertical plane. Two liquids that do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends $90°$ angle at the centre. Radius joining their interface makes an angle $\alpha$ with vertical. Ratio $\frac{d_1}{d_2}$ is:

A $U$ tube with both ends open to the atmosphere is partially filled with water. Oil; which is immiscible with water, is poured into one side until it stands at a distance of $10 \mathrm{mm}$ above the water level on the other side. Meanwhile, the water rises by $65 \mathrm{mm}$ from its original level (see diagram). The density of the oil is:

The pressure at the bottom of a liquid tank is not proportional to the

A $\mathrm{U}$-tube having uniform bore and vertical limbs is filled partially with mercury $\left({\rho }_{\mathrm{Hg}}=13.6\right.$$\mathrm{g} {\mathrm{cc}}^{-1}).$ Water is poured into one of its limbs such that the height of water column is $27.2 \mathrm{cm}$. The rise of mercury in the other limbs is,

An open $U$ tube contains mercury. When $13.6 \mathrm{cm}$ of water is poured into one of the arms of the tube, how high does the mercury rise in the other arm from its initial level ?