Mechanical properties of fluids practice · Medium

Calculate work done required to increase the area of a rectangular film of liquid from $(4 \mathrm{~cm} \times 5 \mathrm{~cm})$ to $(5 \mathrm{~cm} \times 6 \mathrm{~cm})$. (surface tension of the liquid is $0.3 \mathrm{~N} / \mathrm{m}$ )

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm It the entire arrangement is put in a freely falling body (or) elevator, the length of water column in the capillary tube will be

The lower end of a capillary tube of diameter $2.00 \mathrm{~mm}$ is dipped $8.00 \mathrm{~cm}$ below the surface of water in a beaker. What is the pressure required in the tube in order to blow a hemispherical bubble at its end in water? The surface tension of water at the temperature of the experiment is $7.30 \times 10^{-2} \mathrm{~Nm}^{-1} .1$ atmospheric pressure $=1.01 \times 10^5 \mathrm{~Pa}$, density of water $=1000 \mathrm{~kgm}^{-3}, g=9.80 \mathrm{~ms}^{-2}$. Also calculate the excess pressure.

An aircraft has mass $10^6 \mathrm{~kg}$. Its total wing area is $500 \mathrm{~m}^2$. In a level flight with a speed of $1000 \mathrm{~km} / \mathrm{hr}$. Find pressure difference between lower and upper surfaces?

If a drop of mercury having radius $1 \mathrm{~cm}$ is broken into $10^6$ identical small droplets. If surface of mercury is $35 \times 10^{-3} \mathrm{~N} / \mathrm{m}^2$, then find out work done in this process.

If the shearing stress having stress b/w the horizontal layers of water in a river is 1.5 milli newton/${m^2}$ and ${\eta _{\mathrm{water}}} = 1 \times {10^{ - 3}}pa,s$ then the velocity gradient is ${s^{ - 1}}$

Assertion: The shape of liquid drop is spherical.
Reason: The pressure inside liquid drop is greater than that outside it.

Two spherical rain drops with radii in the ratio 1:2 fall with a constant velocity in atmosphere. The ratio of their linear momenta in this situation is

The speed of sound is measured by a resonance tube at the room temperature once by filling the tube with water and then with glycerine as $v_1$ and $v_2$. Which of the following relation relations is/are true in this context?

Water rises to a height $\mathrm{h'}$ in capillary tube. If the length of capillary tube above the surface of water is made less than $\mathrm{h'}$ then:

Assertion:- Surface tension is the property of only liquids
Reason:- Only liquids have free surface in fluids.

The profile of advancing liquid in a tube is a

The density $(\rho)$ of atmospheric air varies with height $(h)$ above the ground according to the relation $\rho=\rho_o e^{-\lambda h}$ where $\lambda$ is a constant. At what height above the ground is the pressure half its value on the surface?

A large $He$ balloon of volume $1425 \mathrm{~m}^3$ is used to lift a pay load of $400 \mathrm{~kg}$. Assume that the balloon maintains constant radius as it rises. How high does it rise? $\rho_0=1.25 \mathrm{~kg} \mathrm{~m}^{-3}$

The pressure at the bottom of a tank of
water is $3P$ where $P$ is the atmospheric
pressure. If the water is drawn out till the
level of water is lowered by one fifth, the
pressure at the bottom of the tank will now
be:

Statement A: To float a body, weight of the displaced liquid is equal to the actual weight of the body.
Statement B: The body will experience no net downward force in that case.

At critical temperature, the surface tension of a liquid is

Increase in pressure at one point of the enclosed liquid in rest is transmitted equally to all other points of liquid". Above statement is in accordance with the

STATEMENT-1 : The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.

STATEMENT-2 : In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

Reynolds number is the ratio of:

If a rain drop starts falling from the cloud
level then before it acquires the terminal
velocity, its acceleration and velocity
respectively

Shear modulus is zero for

Assertion: When the stopcock over the $U$-tube having a large bubble at its one end and a small bubble at the other end is opened, air flows from the large bubble to the small bubble.
Reason: The pressure inside the large bubble is greater than that inside small bubble.

Statement A: An object falling through a viscous medium eventually attains terminal velocity
Statement B: All the rain drops hit the surface of the earth with the same constant velocity

A water drop of radius $1 \mathrm{~cm}$ is broken into 1000 equal droplets. What would be the gain in surface energy, if the surface tension of water is $0.075 \mathrm{Nm}^{-1}$

Assertion: If an object is submerged in fluid at rest, the fluid exerts a force on its surface.
Reason: Force exerted by the fluid at rest has to be parallel to the surface in contact with it.

An air-tight cage with a parrot sitting in it is suspended from the spring balance. The parrot starts flying. The reading of the spring balance will

The area of cross-section of a large tank is $0.5 \mathrm{~m}^2$. It has an opening near the bottom having area of cross-section $1 \mathrm{~cm}^2$. A load of $20 \mathrm{~kg}$ is applied on the water at the top. Find the velocity of the water coming out of the opening at the time when the height of water level is $50 \mathrm{~cm}$ above the bottom. (approx.) (Take $g=10 \mathrm{~m} / \mathrm{s}^2$)

Assertion: When height of a tube is less than liquid rise in the capillary tube, the liquid does not overflow.
Reason: Product of radius of meniscus and height of liquid in capillary tube always remains constant.

A water tank standing on the floor has two small holes punched in the vertical wall one above the other. The holes are $2.4 \mathrm{~cm}$ and $7.6 \mathrm{~cm}$ above the floor. If the jet of water from the holes hit the floor at the same point, then the height of water in the tank is