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:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal’s principle is observed.

Reason R: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.

In the light of the above statements, choose the most appropriate 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
 

A cubical vessel of side $3 \mathrm{cm}$ and mass $150 \mathrm{g}$ is filled with $0.75$ litre of a liquid. The vessel with liquid is placed on a table, then pressure exerted on the table by the vessel 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?

In a hydraulic lift, compressed air exerts a force $F$ on a small piston of radius $3 \mathrm{cm}$. Due to this pressure the second piston of radius $5 \mathrm{cm}$ lifts a load of $1875 \mathrm{kg}$. The value of $F$ is
(Acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$)

An air bubble rises from the bottom of a lake of depth$10.34 \mathrm{m}$ to its surface. Compare the pressure on bubble at the bottom to that on the surface. (Atmospheric pressure $= 0.76 \mathrm{m}$ of Hg, density of Hg $= 13.6\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ and density of water$= {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$).

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?

Distinguish between thrust and pressure.

$U$-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with$10.0 cm$  of water in one arm and$12.5 cm$  of spirit in the other. What is the relative density of spirit ?

A tank, with a square base of area $1.0 m^2$, is divided by a vertical partition has a small hinged door of area $20 c{m}^2$. The tank is filled with water in one compartment, and an acid (of relative density $1.7$) in the other, both to the height of $4.0$. Compute the force necessary to keep the door closed.

A vertical off-shore structure is built to withstand a maximum stress of ${10}^9 pa$ . Is the structure suitable for putting up on top of an oil well in Bombay High ? Take the depth of the sea to be roughly $3 km$, and ignore ocean currents.