Pressure in a Fluid

A submarine is designed to withstand an absolute pressure of 100 atm. How deep can it go below the water surface?

(Consider the density of water $= 1000\text{ kg m}^{-3},\ 1\text{ atm} = 1 \times 10^{5}\text{ Pa}$ and gravitational acceleration $g = 10\text{ m/s}^{2}$)

Given below are two statements:

Statement I: Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.

Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.

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

The pressure at half the depth of a lake is equal to two-third pressure at the bottom of the lake. So the depth 'h' of the lake is ($\rho$ = density of water in the lake, $g$ = acceleration due to gravity, $P_0$ = atmospheric pressure).

When a large bubble rises from bottom of a water lake to its surface, then its radius doubles. If the atmospheric pressure is equal to the pressure of height $H$ of a certain water column then the depth of lake will be

Two cylindrical vessels of equal cross sectional area of $2\text{ m}^{2}$ contain water upto heights 10 m and 6 m, respectively. If the vessels are connected at their bottom then the work done by the force of gravity is (Density of water is $10^{3}\text{ kg/m}^{3}$ and $g = 10\text{ m/s}^{2}$)

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of $100\text{ cm}^{2}$ with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density $1.5 \times 10^{3}\text{ kg/m}^{3}$. What force one needs to apply on the hinged door so that it does not get opened? (Acceleration due to gravity $= 10\text{ m/s}^{2}$)

The temperature of an air bubble while rising from bottom to surface of a lake remains constant but diameter is doubled. If pressure on the surface is $h$ meter of mercury column and relative density of mercury is ' $\rho$ ' then the depth of the lake is

Given below are two statements:

Statement I: When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $P_1 - P_2 = \rho g (h_2 - h_1)$.

Statement II: In ventury tube shown $2gh = v_1^2 - v_2^2$

In the light of the above statements, choose the most appropriate answer from the options given below.

Mercury is filled in a tube of radius $2\text{ cm}$ up to a height of $30\text{ cm}$. The force exerted by mercury on the bottom of the tube is _________ N.

(Given, atmospheric $= 10^{5}\text{ N m}^{-2},\ g = 10\text{ m s}^{-2},\ \pi = \frac{22}{7})$pressure, density of mercury

$= 1.36 \times 10^{4}\text{ kg m}^{-3}$

When an air bubble rises from the bottom of lake to the surface, its radius is doubled. The atmospheric pressure is equal to that of a column of water of height ' $H$ '. The depth of the lake is

A drum of radius ' $R$ ' full of liquid of density ' $d$ ' is rotated at angular velocity ' $\omega$ ' $\text{rad/s}$. The increase in pressure at the centre of the drum will be

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:

An air bubble of volume $1\text{ cm}^{3}$ rises from the bottom of a lake $40\text{ m}$ deep to the surface at a temperature of $12^\circ\text{C}$. The atmospheric pressure is $1 \times 10^{5}\text{ Pa}$ the density of water is $1000\text{ kg/m}^{3}$ and $g = 10\text{ m/s}^{2}$. There is no difference of the temperature of water at the depth of $40\text{ m}$ and on the surface. The volume of air bubble when it reaches the surface 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:

Two cylindrical vessels of equal cross-sectional area $16\text{ cm}^{2}$ contain water upto heights $100\text{ cm}$ and $150\text{ cm}$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take, density of water $= 10^{3}\text{ kg/m}^{3}$ and $g = 10\text{ m s}^{-2}$ ]:

The pressure acting on a submarine is 3 $\times$ 105 Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be:

(Assume that atmospheric pressure is 1 $\times$ 105 Pa and density of water is 103 kg m${}^{-3}$, g = 10 ms${}^{-2}$)

A barometer is constructed using a liquid (density = $760\text{ kg/m}^{3}$). What would be the height of the liquid column, when a mercury barometer reads 76 cm?

(density of mercury = $13600\text{ kg/m}^{3}$)

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x1 and in the other, x2. When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is:

Two liquids of densities $\rho_1$ and $\rho_2$ ($\rho_2$ = 2$\rho_1$) are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing)

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is $\omega$ rad s–1. The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be:

A submarine experiences a pressure of 5.05 × 106 Pa at a depth of d1 in a sea. When it goes further to a depth of d2, it experiences a pressure of 8.08 × 106 Pa. Then d2 –d1 is approximately (density of water = 103 kg/m3 and acceleration due to gravity = 10 ms–2):

In a u-tube as shown in the fig. water and oil are in the left side and right side of the tube respectively. The heights from the bottom for water and oil columns are 15 cm and 20 cm respectively. The density of the oil is

[take $\rho_{\text{water}} = 1000\text{ kg/m}^{3}$]

When a large bubble rises from bottom of a water lake to its surface, then its radius doubles. If the atmospheric pressure is equal to the pressure of height $H$ of a certain water column, then the depth of lake will be

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be:

When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes $\frac{5r}{4}$ Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature):

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 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is