Mechanical properties of fluids practice · Mixed difficulty

The ratio of radii of two bubbles is $2: 1$ What is the ratio of excess pressures inside them?

Two spherical soap bubbles of radii $a$ and $b$ in vacuum coalesce under isothermal conditions. The resulting bubble has a radius given by

When the temperature is increased, the angle of contact of a liquid

Assertion: The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection.
Reason: Flow rate is independent of pressure exerted by the thumb of the doctor.

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.

How much pressure will a man of weight $80 \mathrm{~kgf}$ exert on the ground when he is lying on the ground. Given that the area of the body of the man is $0.6 \mathrm{~m}^2$ and that of a foot is $80 \mathrm{~cm}^2$.

An atmosphere,

A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is $0.075\,\,N/m.$ In this process the gain in surface energy will be

The depth of water at which air bubble of radius 0.4 mm remains in equilibrium is $\left( {{T_{\mathrm{water}}} = 72 \times {{10}^{ - 3}}\,\,N/m} \right)$

The work done in blowing a spherical soap bubble of diameter 2 cm will be (T = 0.02 N/m)

Assertion: Water drop stick to glass surface.
Reason: Water have properties of surface tension.

Assertion:- Machine parts are jammed in winter.
Reason:-The viscosity of lubricant used in machine part decrease at low temperature.

Assertion: Sometimes insects can walk on water.
Reason: The gravitational force on insect is balanced by force due to surface tension.

Assertion: A surface tension experiment with a capillary tube is done on an artificial satellite then the rise of liquid in the capillary is upto full length of the tube.
Reason: The value of $g_{\text {effective}}$ is zero on an artificial satellite.

Water is flowing in a pipe of radius $1 {~cm}$ with an average velocity $20 {~cm} / {s}$. If coefficient of viscosity of water is $10^{-3} {~kg} {~m}^{-1} {~s}^{-1}$ and density is $10^3 {~kg} / {m}^3$, then the nature of flow is

What would be the pressure inside a small air bubble of $1.0\,mm$ radius situated just below the surface of water? $\left[ {T = 72 \times {{10}^{ - 3}}\,N/m;{\rho _0} = 1.013 \times {{10}^5}\frac{N}{{{m^2}}}} \right]$

A piece of wood is floating in water kept in bottle. The bottle is connected to an air pump. Neglect the compressibility of water. When more air is pushed into the bottle from the pump, the piece of wood will float with

While measuring surface tension of water using capillary
rise method, height of the lower meniscus from free
surface of water is 3 cm while inner radius of capillary tube is found to be 0.5 cm. Then, compute tension of
water using this data (take, contact angle between glass
and water as $0$ and $g = 9.81 \text{m/s}^2)$

A horizontal tube has different cross-sectional areas at points $A$ and $B$. The diameter of $A$ is $4 \mathrm{~cm}$ and that of $B$ is $2 \mathrm{~cm}$. Two manometer limbs are attached at $A$ and $B$. When a liquid of density $8.0 \mathrm{~g} \mathrm{~cm}^{-3}$ flows through the tube, the pressure difference between the limbs of the manometer is $8 \mathrm{~cm}$. Calculate the rate of flow of the liquid in the tube.

Calculate the diameter of a capillary tube in which mercury is depressed by $1.21 \mathrm{~cm}$. Given surface tension for mercury is $540 \times 10^{-3} \mathrm{~Nm}^{-1}$, the angle of contact with glass is $140^{\circ}$ and density of mercury is $13.6 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$.

Height $h$ of water raised in a capillary tube of radius $r$ depends on $r$ as

An aeroplane of mass $3 \times {10^4}$ kg and total wing area of $120{\mathrm{m}^2}$ is in a level flight at some height. The difference in pressure between the upper and lower surface of its wings in kilo pascals is $\left( {\mathrm{g} = 10\mathrm{m}{\mathrm{s}^{ - 2}}} \right)$

Assertion: A wooden piece floats half submerged in a tank of water. If the system accelerates up then the wooden piece will remain half submerged.
Reason: When the system starts accelerating up, then effective $g$ will be same for both water and wooden piece.

A ball floats on the surface of water in a container exposed to the atmosphere. Will the ball remain immersed at its former depth or will it sink or will it rise if the container is covered and the air is removed?

At which of the following temperatures, the value of surface tension of water is minimum?

A liquid of specific gravity 1.5 is observed to rise $3.0 \mathrm{~cm}$ in a capillary tube of diameter $0.50 \mathrm{~mm}$ and the liquid wets the surface of the tube. Calculate the excess pressure inside a spherical bubble of $1.0 \mathrm{~cm}$ diameter blown from the same liquid. Angle of contact $=0^{\circ}$.

The level of water in a tank is 5 m high. A hole of area of cross section $1\,c{m^2}$ is made at the bottom of the tank. The rate of leakage of water from the hole in ${m^3}{s^{ - 1}}$ is $\left( {g = 10\,m{s^{ - 2}}} \right)$

Two soap bubbles $A$ and $B$ are formed at the two open ends of a tube. The bubble $A$ is smaller than bubble$B$. Valve and air can flow freely between the bubbles, then

Assertion:- Bemoulli’s theorem holds true for ideal fluids in laminar flow.
Reason:- In laminar flow, viscous force is not exerted.