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 spherical marble of radius $1 \mathrm{cm}$ is stuck in a circular hole of radius slightly smaller than its own radius (for calculation purpose, both can be taken same) at the bottom of a bucket of height $40 \mathrm{cm}$ and filled with water up to $10 \mathrm{cm}$. If the mass of the marble is $20 \mathrm{g}$, the net force on the marble due to water is close to

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

A submarine has a window of area $30\times 30 {\mathrm{cm}}^2$ on its ceiling and is at a depth of $100 \mathrm{m}$ below sea level in a sea. If the pressure inside the submarine is maintained at the sea-level atmosphere pressure, then the force acting on the window is (consider density of sea water $=1.03\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$):

Consider two wires of same material having their ratio of radii to be $2:1$. If these two wires are stretched by equal force, the ratio of stress produced in them is :

A healthy adult of height $1.7 \mathrm{m}$ has an average blood pressure (BP) of $100 \mathrm{mm}$ of $\mathrm{Hg}$. The heart is typically at a height of $1.3 \mathrm{m}$ from the foot. Take, the density of blood to be ${10}^3 \mathrm{kg}/{\mathrm{m}}^3$ and note that $100 \mathrm{mm}$ of $\mathrm{Hg}$ is equivalent to $13.3\mathrm{kPa}$ (kilo pascals). The ratio of BP in the foot region to that in the head region is close to
 

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,