Mechanical properties of fluids practice · Medium

Three capillaries of lengths $l, 2 l$ and $l / 2$ are connected in series. Their radii are $r, r / 2$ and $r / 3$ respectively. If stream-line flow is maintained and the pressure difference across the first capillary tube is $p_1$, find the pressure difference across (i) the second and (ii) the third capillary tube.

A solid shell loses half of its weight in water. If relative density of shell is 5 , then what fraction of its volume is hollow?

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

What is the pressure inside a vapour bubble of radius $10^{-3} \mathrm{~m}$ formed in boiling water? Surface tension of water at 100 is $0.059 \mathrm{~Nm}^{-1}$ and $1 \mathrm{~atm}=101325 \mathrm{~Nm}^{-2}$.

Angle of contact of a liquid with a solid depend on

A metal ball weighs $0.096 \mathrm{~N}$. When suspended in water it has an apparent weight of $0.071 \mathrm{~N}$. Find the density of the metal.

Check the dimensional consistency of the Poiseuille's formula for the laminar flow in a tube: $Q=\frac{\pi R^4\left(p_1-p_2\right)}{8 \eta l}$

Given below are two statements: one is labelled as
Assertion A and the other is labelled as Reason R

Assertion A : A spherical body of radius $\left( {5 \pm 0.1} \right)\,\,{\text{mm}}$ having a particular density is falling through a
liquid of constant density. The percentage error in
the calculation of its terminal velocity is 4%.

Reason R : The terminal velocity of the spherical
body falling through the liquid is inversely
proportional to its radius.

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

Assertion: The upper surface of the wings of an aeroplane is made convex and the lower surface is made concave.
Reason: The air currents at the top have a smaller velocity and thus less pressure at the bottom than at the top.

The working of venturimeter is based on

A: A hydrogen filled balloon stops raising after it has attained a certain height in the sky
R: The buoyancy of an object depends both on the material and shape of the object

If $\rho$ is the density and $\eta$ is coefficient of viscosity of fluid which flows with a speed $v$ in the pipe of diameter $d,$ the correct formula for Reynolds number ${R_e}$ is:

Eight small raindrops each of radius $1 {~mm}$, come down with a terminal velocity of $10 {~cm} / {s}$. They coalesce to form a bigger drop. The terminal velocity of the bigger drop will be

Which of the following is not the unit of surface tension?

Assertion: The flow of fluid is said to be steady if at any given point, the velocity of each passing fluid particle do not remain constant.
Reason: The path taken by a fluid particle under a steady flow is a turbulent.

Two solids $A$ and $B$ float in water. It is observed that A floats with$\frac{1}{2}$ of its body immersed in water and $B$ floats with $\frac{1}{4}$ of its volume above the water level. The ratio of the density of $A$ to that of $B$is

If a large drop of radius $2 \mathrm{~cm}$ is splitted into 8 identical small droplets. Find out work done in this process if surface tension of liquid is $\mathrm{T ~dyne}/ \mathrm{cm}$.

Statement-1: Coefficient of viscosity of a liquid decreases while that of a gas increase, with increasing temperature.
Statement-2: Density of a liquid and that of a gas vary in opposite manner with increase in temperature.

Assertion: It is better to wash the clothes in hot soap solution.
Reason: The surface tension of cold solution is more than the surface tension of hot solution.

Equal mass of three liquids are kept in three identical cylindrical vessels A, B and C. Their densities are $\rho_A, \rho_B, \rho_C$ with $\rho_A<\rho_B<\rho_C$. The force on the base will be

An air bubble of radius $2.0 \mathrm{~mm}$ is formed at the bottom of a $3.3 \mathrm{~m}$ deep river. Calculate the radius of the bubble as it comes to the surface. Atmospheric pressure $=1.0 \times 10^5 \mathrm{~Pa}$ and density of water $=1000 \mathrm{~kg} \mathrm{~m}^{-3}$.

A water film is made between two straight parallel wires of length 10 cm separated by 5 mm from each other. If the distance between the wires is increased by 2 mm. How much work will be done? Surface tension for water is $72\mathrm{dyne c}{\mathrm{m}^{ - 1}}$

The gauge pressure of water in a tank at its bottom is $3.92 \times 10^5 \, {~Pa}$. If the density of water is $1000\, {~kg} / {m}^3$, then the water emerges from the orifice at bottom in the tank with velocity

Assertion:- Smaller drops of liquid resist deforming forces better than the larger drops.
Reason:- Excess pressure inside a drop is directly proportional to its surface area.

Assertion(A): A solid sphere and a hollow sphere both of same material are immersed in a liquid, then change in weight in both the spheres will be same.

Reason(R): Upthrust depends upon the volume of the solid immersed not the mass.

Assertion: Hydrostatic pressure is not a vector quantity.
Reason: Pressure is force divided by area, and force is a vector quantity.

The fraction of a floating object of volume ${V_0}$ and density ${d_0}$ above the surface of a liquid of density $d$ will be

Formation of lead shots use the property of:

A liquid is flowing into a tube of truncated cone shape. Identify the correct statement from the following.

Bunsen's burner works on the principle of: