Fluid Mechanics — JEE Main PYQs

A liquid column of height 0.04 cm balances excess pressure of soap bubble of certain radius. If density of liquid is $8\times 10^3\mathrm{kg}{\mathrm{m}}^{-3}$ and surface tension of soap solution is $0.28{\mathrm{Nm}}^{-1}$, then diameter of the soap bubble is ____ c …

A cube of ice floats partly in water and partly in kerosene oil. The radio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil $=0.8$, specific gravity of ice $=0.9$ )

Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of $10\mathrm{cm}/\mathrm{s}$. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be ______ …

A sphere of relative density $\sigma$ and diameter D has concentric cavity of diameter d. The ratio of $\frac{\mathrm{D}}{\mathrm{d}}$, if it just floats on water in a tank is:

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is :

A spherical ball of radius $1\times 10^{-4}\mathrm{m}$ and density $10^5\mathrm{kg}/{\mathrm{m}}^3$ falls freely under gravity through a distance $h$ before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value …

The reading of pressure metre attached with a closed pipe is $4.5\times 10^4\mathrm{N}/{\mathrm{m}}^2$. On opening the valve, water starts flowing and the reading of pressure metre falls to $2.0\times 10^4\mathrm{N}/{\mathrm{m}}^2$. The velocity of water is found to …

A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be :

Given below are two statements :
Statement (I) :Viscosity of gases is greater than that of liquids.
Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities.
In the light of the above statements, choose the most appropriate answer from th …

Given below are two statements:

Statement I: If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.

Statement II: If a capillary tube is immersed first in cold water and then in hot water, the height …

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $70{\mathrm{ms}}^{-1}$ and $65{\mathrm{ms}}^{-1}$ respectively. If the wing area is $2{\mathrm{m}}^2$ the lift of the wing is $\_\_\_\_$ N.
(Given density …

A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?

A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :

A plane is in level flight at constant speed and each of its two wings has an area of $40{\text{ m}}^2$. If the speed of the air is $180\text{ km/h}$ over the lower wing surface and $252\text{ km/h}$ over the upper wing surface, the mass of the plane is ______ kg. (Take air dens …

A big drop is formed by coalescing 1000 small identical drops of water. If ${\mathrm{E}}_1$ be the total surface energy of 1000 small drops of water and ${\mathrm{E}}_2$ be the surface energy of single big drop of water, the ${\mathrm{E}}_1$ : ${\mathrm{E}}_2$ is …

A small spherical ball of radius r, falling through a viscous medium of negligible density has terminal velocity 'v'. Another ball of the same mass but of radius $2r$, falling through the same viscous medium will have terminal velocity:

A hydraulic automobile lift is designed to lift vehicles of mass 5000 kg. The area of cross section of the cylinder carrying the load is $250{\mathrm{cm}}^2$. The maximum pressure the smaller piston would have to bear is [Assume $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$]:

An air bubble of diameter 6 mm rises steadily through a solution of density $1750\mathrm{kg}/{\mathrm{m}}^3$ at the rate of $0.35\mathrm{cm}/\mathrm{s}$. The co-efficient of viscosity of the solution (neglect density of air) is $\_\_\_\_$ Pas (given, …

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 …

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $2.0{\mathrm{cm}}^2$. The area of cross section at the outlet is $10{\mathrm{mm}}^2$. If the piston is pushed at a speed of $4\mathrm{cm}{\mathrm{s}}^{-1}$, the speed of …

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 correc …

Glycerine of density $1.25\times 10^3\mathrm{kg}{\mathrm{m}}^{-3}$ is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends is $10{\mathrm{cm}}^2$ and $5{\mathrm{cm}}^2$ and pressure drop across its length is …

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross-section. Cross sectional areas at A is $1.5$ cm${}^2$, and B is $25$ mm${}^2$, if the speed of liquid at B is $60$ cm/s then $(P_A-P_B)$ is :
(Given $P_A$ and $P_B$ are liquid pressures …

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 $(5\pm 0.1)$ mm having a particular density is falling through a liquid of constant density. The percentage error in the calculation of …

There is an air bubble of radius 1.0 mm in a liquid of surface tension $0.075$ Nm${}^{-1}$ and density 1000 kg m${}^{-3}$ at a depth of 10 cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is ______ Pa ($g=10$ ms …

A small ball of mass M and density $\rho$ is dropped in a viscous liquid of density ${\rho }_0$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball?

Eight equal drops of water are falling through air with a steady speed of $10\mathrm{cm}/\mathrm{s}$. If the drops coalesce, the new velocity is:-

The surface tension of soap solution is $3.5\times 10^{-2}{\mathrm{Nm}}^{-1}$. The amount of work done required to increase the radius of soap bubble from 10 cm to 20 cm is $\_\_\_\_$ $\times 10^{-4}\mathrm{J}$.

A mercury drop of radius $10^{-3}\mathrm{m}$ is broken into 125 equal size droplets. Surface tension of mercury is $0.45{\mathrm{Nm}}^{-1}$. The gain in surface energy is:

A Spherical ball of radius 1 mm and density $10.5$ g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density $1.5$ g/cc. Viscous force on the ball when it attains constant velocity is $3696\times 10^{-x}$ N. The value of $x$ is
(Given, $g=9.8$ m/s${}^2$ and …

A spherical drop of liquid splits into 1000 identical spherical drops. If $u_i$ is the surface energy of the original drop and $u_f$ is the total surface energy of the resulting drops, the (ignoring evaporation). $\frac{u_f}{u_i}=\left(\frac{10}{x}\right)$. Then value of …

Surface tension of a soap bubble is $2.0\times 10^{-2}{\mathrm{Nm}}^{-1}$. Work done to increase the radius of soap bubble from 3.5 cm to 7 cm will be : [Take $\pi =\frac{22}{7}$]

A fully loaded boeing aircraft has a mass of $5.4\times 10^5\mathrm{kg}$. Its total wing area is $500{\mathrm{m}}^2$. It is in level flight with a speed of $1080\mathrm{km}/\mathrm{h}$. If the density of air $\rho$ is $1.2\mathrm{kg}{\mathrm{m}}^{-3}$, the …

A metal block of base area $0.20{\mathrm{m}}^2$ is placed on a table, as shown in figure. A liquid film of thickness 0.25 mm is inserted between the block and the table. The block is pushed by a horizontal force of 0.1 N and moves with a constant speed. If the viscosity of the …

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, 5 cm. If the tube is dipped in a similar manner in another liquid B of surface tension and density double the values of liquid A, the height of liquid column raised in …

If 1000 droplets of water of surface tension $0.07$ N/m. having same radius 1 mm each, combine to from a single drop. In the process the released surface energy is-
(Take $\pi =\frac{22}{7}$)

The surface of water in a water tank of cross section area $750{\mathrm{cm}}^2$ on the top of a house is $h\mathrm{m}$. above the tap level. The speed of water coming out through the tap of cross section area $500{\mathrm{mm}}^2$ is $30\mathrm{cm}/\mathrm{s}$. At that i …

The velocity of a small ball of mass 0.3 g and density $8\mathrm{g}/\mathrm{cc}$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $1.3\mathrm{g}/\mathrm{cc}$, then the value of viscous force acting on t …

The diameter of an air bubble which was initially 2 mm, rises steadily through a solution of density $1750$ kg m${}^{-3}$ at the rate of $0.35$ cms${}^{-1}$. The coefficient of viscosity of the solution is _____ poise (in nearest integer). (the density of air is negligible).

Consider a cylindrical tank of radius 1 m is filled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 m from the bottom. A force of $5\times 10^5\mathrm{N}$ is applied an the top surfac …

A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of …

A drop of liquid of density $\rho$ is floating half immersed in a liquid of density $\sigma$ and surface tension $7.5\times 10^{-4}{\mathrm{Ncm}}^{-1}$. The radius of drop in cm will be : (Take : $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$ )

A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne $/\mathrm{cm}$, then the gain in surface energy upto first decimal place will be :
[Given $\pi =3.14$]

A water drop of radius $1\mu \mathrm{m}$ falls in a situation where the effect of buoyant force is negligible. Coefficient of viscosity of air is $1.8\times 10^{-5}{\mathrm{Nsm}}^{-2}$ and its density is negligible as compared to that of water $10^6{\mathrm{gm}}^{-3}$. T …

A liquid of density $750{\mathrm{kgm}}^{-3}$ flows smoothly through a horizontal pipe that tapers in cross-sectional area from ${\mathrm{A}}_1=1.2\times 10^{-2}{\mathrm{m}}^2$ to $A_2=\frac{A_1}{2}$. The pressure difference between the wide and narrow sections of the …

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

Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.
Reason R:
Coefficient of viscosity …

A small spherical ball of radius 0.1 mm and density $10^4\mathrm{kg}{\mathrm{m}}^{-3}$ falls freely under gravity through a a distance $h$ before entering a tank of water. If after entering the water the velocity of ball does not change and it continue to fall with same c …

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 ${\mathrm{R}}_{\mathrm{e}}$ is :

An ideal fluid of density $800{\mathrm{kgm}}^{-3}$, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to $\frac{\mathrm{a}}{2}$. The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, …

The velocity of a small ball of mass ' $m$ ' and density ${\mathrm{d}}_1$, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is ${\mathrm{d}}_2$, then the viscous force acting on the ball, will be :