Fluid Mechanics — JEE Main PYQs

Given below are two statements:
Statement I: Pressure of fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to inter …

When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by $1\%$ each, then the height of the liquid in the tube …

Surface tension of two liquids (having same densities), ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, are measured using capillary rise method utilizing two tubes with inner radii of $r_1$ and $r_2$ where $r_1>r_2$. The measured liquid heights in these tubes are …

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is $20\mathrm{cm}/\mathrm{s}$. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be
____ $\mathrm{cm}/\mathrm{s}$.

A small metallic sphere of diameter 2 mm and density $10.5$ g/cm³ is dropped in glycerine having viscosity 10 Poise and density $1.5$ g/cm³ respectively. The terminal velocity attained by the sphere is $\_\_\_\_$ cm/s.
($\pi =\frac{22}{7}$ and $g=10$ m/s²)

Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of $10\mathrm{cm}/\mathrm{s}$ coalesce to form a bigger drop. The terminal velocity of bigger drop is ______ $\mathrm{cm}/\mathrm{s}$.

A cubical block of density ρ_b = 600 kg/m³ floats in a liquid of density ρ_e = 900 kg/m³. If the height of block is H = 8.0 cm then height of the submerged part is ____ cm.

A soap bubble of surface tension $0.04\mathrm{N}/\mathrm{m}$ is blown to a diameter of 7 cm. If $(15000-\mathrm{x})\mu \mathrm{J}$ of work is done in blowing it further to make its diameter 14 cm, then the value of x is ____.
( $\pi =22/7$ )

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at $A$ and $B$ are $6{\mathrm{cm}}^2$ and $3{\mathrm{cm}}^2$ respectively.
The rate of flow will b …

The surface tension of a soap bubble is $0.03\mathrm{N}/\mathrm{m}$. The work done in increasing the diameter of bubble from 2 cm to 6 cm is $\alpha \pi \times 10^{-4}\mathrm{J}$. The value of $\alpha$ is ____. (Take $\pi =3.14$)

If an air bubble of diameter 2 mm rises steadily through a liquid of density $2000\mathrm{kg}/{\mathrm{m}}^3$ at a rate of $0.5\mathrm{cm}/\mathrm{s}$, then the coefficient of viscosity of liquid is $\_\_\_\_$ Poise. (Take $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

The surface tension of a soap solution is $3.5\times 10^{-2}$ N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is $\alpha \times 10^{-6}$ J. The value of $\alpha$ is _____ . ($\pi =22/7$)

A water spray gun is attached to a hose of cross sectional area $30{\mathrm{cm}}^2$. The gun comprises of 10 perforations each of cross sectional area of $15{\mathrm{mm}}^2$. If the water flows in the hose with the speed of $50\mathrm{cm}/\mathrm{s}$, calculate the speed …

Eight mercury drops, each of radius $r$, coalesce to form a bigger drop. The surface energy released in this process is ______. (S is the surface tension of mercury).

A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is $528$ dm${}^3$ (dm: decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm below the top of water level, then horizontal rang …

A liquid of density $600\mathrm{kg}/{\mathrm{m}}^3$ flowing steadily in a tube of varying cross-section. The cross-section at a point A is $1.0{\mathrm{cm}}^2$ and that at B is $20{\mathrm{mm}}^2$. Both the points A and B are in same horizontal plane, the speed of t …

A spherical liquid drop of radius R acquires the terminal velocity ${\mathrm{v}}_1$ when falls through a gas of viscosity $\eta$. Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity ${\mathrm{v}}_2$ falling through the same gas. The …

A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is $\alpha \times 10^{-6}\mathrm{J}$. The value of $\alpha$ is ____. (Take surface tension of liquid $=0.08\mathrm{N}/\mathrm{m}$)

A tube is filled with water and a wooden cube $10\mathrm{cm}\times 10\mathrm{cm}\times 10\mathrm{cm}$ is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged …

Two soap bubbles of radius 2 cm and 4 cm, respectively, are in contact with each other. The radius of curvature of the common surface, in cm, is ______.

A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be
(consider g …

The tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is $2\mathrm{m}/\mathrm{s}$, then velocity of water leaving the point (2) will be :

Given below are two statements:

Statement-I : The hot water flows faster than cold water.

Statement-II : Soap water has higher surface tension as compared to fresh water.

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

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is ${\mathrm{P}}_1$. The reading of the pressure gauge falls to ${\mathrm{P}}_2$ when the valve is opened. The speed of water flowing in the pipe is propo …

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension $0.095\mathrm{J}/{\mathrm{m}}^2$ and density $10^3\mathrm{kg}/{\mathrm{m}}^3$. The difference between pressure inside the bubble and atmospheric pres …

The fractional compression $\left(\frac{\Delta V}{V}\right)$ of water at the depth of 2.5 km below the sea level is $\_\_\_\_$ %. Given, the Bulk modulus of water $=2\times 10^9{\mathrm{Nm}}^{-2}$, density of water $=10^3\mathrm{kg}{\mathrm{m}}^{-3}$, acceleration due to gr …

In a hydraulic lift, the surface area of the input piston is $6{\mathrm{cm}}^2$ and that of the output piston is $1500{\mathrm{cm}}^2$. If 100 N force is applied to the input piston to raise the output piston by 20 cm , then the work done is $\_\_\_\_$ kJ.

a 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water?
(Given : density of water $=1000\mathrm{kg}{\mathrm{m}}^{-3}$ )

In the experiment for measurement of viscosity '$\eta$' of given liquid with a ball having radius R, consider following statements.
A. Graph between terminal velocity V and R will be a parabola
B. The terminal velocities of different diameter balls are constant for a given liquid …

Consider following statements:
A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid.
B. As the temperature of liquid rises, the coefficient of viscosity increases.
C. As the temperature of gas incr …

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density $1000\mathrm{kg}/{\mathrm{m}}^3$. If the pressure inside the bubble is $2100\mathrm{N}/{\mathrm{m}}^2$ greater than the atmospheric pressure, then the surface tension of …

The amount of work done to break a big water drop of radius 'R' into 27 small drops of equal radius is 10 J. The work done required to break the same big drop into 64 small drops of equal radius will be :-

Two water drops each of radius 'r' coalesce to form a bigger drop. If 'T' is the surface tension, the surface energy released in this process is :

Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area $0.5{\mathrm{m}}^2$. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the wate …

A solid steel ball of diameter 3.6 mm acquired terminal velocity $2.45\times 10^{-2}\mathrm{m}/\mathrm{s}$ while falling under gravity through an oil of density $925\mathrm{kg}{\mathrm{m}}^{-3}$. Take density of steel as $7825\mathrm{kg}{\mathrm{m}}^{-3}$ and g as …

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is $n$ times the volume of the bubble B, then, the value of $n$ is ____.

Two liquids A and B have ${\theta }_{\mathrm{A}}$ and ${\theta }_{\mathrm{B}}$ as contact angles in a capillary tube. If $K=\cos {\theta }_A/\cos {\theta }_B$, then identify the correct statement:

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension $70\mathrm{dyn}/\mathrm{cm}$ and glass water contact angle $\simeq 0^{\circ }$ ) with $30^{\circ }$ inclined with vertical. The length of water risen in the capillary is ____ cm .
(Take …

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balan …

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of $100{\mathrm{cm}}^2$ with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with …

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : R = Radius of bubble, $S=$ Surface tension of bubble)

Given below are two statements :

Statement I: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.

In the light of t …

Mercury is filled in a tube of radius 2 cm up to a height of 30 cm. The force exerted by mercury on the bottom of the tube is ____ N.
(Given, atmospheric pressure $=10^5{\mathrm{Nm}}^{-2}$, density of mercury …

Given below are two statements :

Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $P_1-P_2=\rho \mathrm{g}\left({\mathrm{h}}_2-{\mathrm{h}}_1\right)$
Statement II : In ventury tube shown …

A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/cm then the new radius is ______ cm. Take: $\left(\pi =\frac{22}{7}\right)$.

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is ____ N …

Given below are two statements :

Statement-I: When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be $0^{\circ }$.
Statement-II: The contact angle between a solid and a liquid is a property of the material of …

A small ball of mass $m$ and density $\rho$ is dropped in a viscous liquid of density ${\rho }_0$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $\frac{10}{x}$. The value of $x$ is ______.

Correct Bernoulli's equation is (symbols have their usual meaning) :