Mechanical properties of fluids practice · Medium

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.

Which of the following will vanish for a fluid in a space where there is no gravity?

A plane of mass $3250 {~g}$ is in level flight at a constant speed and each wing has an area of $25 {~m}^2$. During flight the speed of the air is $216 \,{kmh}^{-1}$ over the lower wing surface and $252 \,{kmh}^{-1}$ over the upper wing surface of each wing of aeroplane. Take density of air $=1 \,{kgm}^{-3}$ and $g=10 {~ms}^{-2}$.
If a plane is in level flight with a speed of $360 \,{kmh}^{-1}$ then the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface is

Assertion:- Soil particles inside water are freely placed but they stick together when taken out of water.
Reason:- Thin filens formed creates pressure difference.

If two soap bubbles of different radii are in communication with each other, then

Consider the following two statement $\mathrm{A}$ and $\mathrm{B}$, and identify the correct choice in the given answers

A : The excess pressure inside a small liquid drop is more than that of a big drop.

B : As the aeroplane moves fast on the runway for take off the pressure is more on the upper surface of its wings and less on the bottom surface of the wings.

Assertion: The velocity of the rain drops increases only upto a limit as they start their journey towards the surface of the earth.
Reason: The rain drops attain terminal velocity in the due course of time, while falling through air.

The reading of spring balance when a block is suspended from it in air is 60N. This reading is changed to 40N when the block is submerged in water. The specific gravity of the block must therefore

The value of g at a place decreases by 2%. The barometric
height of mercury:

Which of the following statements is not true about surface tension?

There is a hole of area $A$ at the bottom of a cylindrical vessel. Water is filled upto a height $h$ and water flows out in $t$ sec. If water is filled to a height $4h$, then it will flow out in time

A spherical ball of radius $3.0 \times 10^{-4} \mathrm{~m}$ and density $10^4 \mathrm{~kg} / \mathrm{m}^3$ falls freely under gravity through a distance ' $h$ ' before entering a tank of water. If after entering the water the velocity of the ball does not change, $h$ is (Viscosity of water is $10^{-5} \frac{\mathrm{Ns}}{\mathrm{m}^2},\quad g=10 \mathrm{~m} / \mathrm{s}^2$)

A circular frame of wire having radius $r$ is floating on the surface of a liquid having surface tension $\sigma$. The additional force other than its weight, required to pull out the frame from the liquid is

If 2 bubble of radius $r_1 \,\&\, r_2$ are combined then find radius of common surface

An application of Bernoulli’s equation for fluid flow is found in

An object of density $d_0$ kept deep inside water of density $d_\omega$. Its is then released from rest. During the time it moves a vertical distance $h$ with in the water.

Bernoulli's equation for steady, non-viscous, incompressible flow expresses the;

Statement-1: When a soda water bottle falls freely from a height $h$, the gas bubble rises in water from the bottom.
Statement-2: Air is lighter than liquid.

The work done to blow a bubble is W. The extra work to be done to double it radius is

A minute spherical air bubble is rising slowly through a column of mercury contained in a deep jar. If the radius of the bubble at a depth of $100 \mathrm{~cm}$ is $0.1 \mathrm{~mm}$, calculate its depth where its radius is $0.126 \mathrm{~mm}$, given that the surface tension of mercury is $567 \mathrm{~dyne} / \mathrm{cm}$. Assume that the atmospheric pressure is $76 \mathrm{~cm}$ of mercury.

1000 drops of water all of same size join together to form a single drop and the energy released raises the temperature of the drop. Given that $T$ is the surface tension of water, $r$ the radius of each small drop, $\rho$ the density of liquid, $J$ the mechanical equivalent of heat. What is the rise in temperature?

A boat carrying a number of large stones is floating in a water tank. What would happen to the water level, if a few stones are unloaded into water?

One of the units earlier used for expressing pressure was called bar. 1 bar is equivalent to: