Fluid Mechanics — JEE Advanced PYQs

A container of height 2 m, length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates (${\mathrm{M}}_1$ and ${\mathrm{M}}_2$) which extend far beyond the vertical walls in all directions. The container is partitioned into two eq …

Two large, identical water tanks, 1 and 2, kept on the top of a building of height $H$, are filled with water up to height $h$ in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as t …

A table tennis ball has radius $(3/2)\times 10^{-2}\mathrm{m}$ and mass $(22/7)\times 10^{-3}\mathrm{kg}$. It is slowly pushed down into a swimming pool to a depth of $d=0.7\mathrm{m}$ below the water surface and then released from rest. It emerges from the water surf …

A spherical soap bubble inside an air chamber at pressure $P_0=10^5\mathrm{Pa}$ has a certain radius so that the excess pressure inside the bubble is $\Delta P=144\mathrm{Pa}$. Now, the chamber pressure is reduced to $8P_0/27$ so that the bubble radius and its excess …

An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius 0.1 mm is dipped vertically into the liquid through the airtight piston hole, as shown in the figure. The air in the container is isothermally compressed from …

An ideal gas of density $\rho =0.2kg{m}^{-3}$ enters a chimney of height h at the rate of $\alpha =0.8kg{s}^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_1=0.1m^2$ and the upper end is …

A bubble has surface tension $S$. The ideal gas inside the bubble has ratio of specific heats $\gamma =\frac{5}{3}$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $P_{a1}$, the radius of the bubble is fou …

A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density $2.5\mathrm{gm}/\mathrm{cc}$. Initially the …

A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density $2.5\mathrm{gm}/\mathrm{cc}$. Initially the …

A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration $a$ along a fixed inclined plane with angle $\theta =45^{\circ }$. ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are pressures at points 1 and 2, respectively, loc …

An open-ended U-tube of uniform cross-sectional area contains water (density $10^3\mathrm{kg}{\mathrm{m}}^{-3}$). Initially the water level stands at 0.29 m from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density $800\mathrm{kg}{\mathrm{m}}^{-3}$ is …

As shown schematically in the figure, two vessels contain water solutions (at temperature T) of potassium permanganate $\left({\mathrm{KMnO}}_4\right)$ of different concentrations $n_1$ and $n_2\left(n_1>n_2\right)$ molecules per unit volume with …

When water is filled carefully in a glass, one can fill it to a height $h$ above the rim of the glass due to the surface tension of water. To calculate h just before water starts flowing, model the shape of the water above the rim as a disc of thickness h having semicircular edge …

A train with cross-sectional area $S_t$ is moving with speed $v_t$ inside a long tunnel of cross-sectional area $S_0$ ($S_0=4S_t$). Assume that almost all the air (density $\rho$) in front of the train flows back between its sides and the walls of the tunnel. Also, the air flow …

A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total mass is 480 kg. Its effective volume giving the balloon its buoyancy is $V$. The balloon is floating at an equilibrium height of 100 m. When $N$ number of sandbags are thrown out …

A spherical bubble inside water has radius $R$. Take the pressure inside the bubble and the water pressure to be $p_0$. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes $(R-a)$. For $a\ll R$ the magnitude of the work done in the process i …

A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T1 and T2 of different materials having water contact angles of 0° and 60°, respectively. The capillary tube is dipped vertically in water in two different configurations, case I and II as shown in f …

Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity $u_0$. Which of the following statements is (are) …

A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $\sigma$. The angle of contact between water and the wal …

A drop of liquid of radius $\mathrm{R}=10^{-2}\mathrm{m}$ having surface tension $\mathrm{S}=\frac{0.1}{4\pi }{\mathrm{Nm}}^{-1}$ divides itself into $K$ identical drops. In this process the total change in the surface energy $\Delta U=10^{-3}\mathrm{J}$. If …

Consider two solid spheres P and Q each of density 8 gm cm${}^{-3}$ and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm${}^{-3}$ and viscosity $\eta =3$ poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm${}^{-3}$ an …

Two spheres P and Q of equal radii have densities ${\rho }_1$ and ${\rho }_2$, respectively. The spheres are connected by a massless string and placed in liquids $L_1$ and $L_2$ of densities ${\sigma }_1$ and ${\sigma }_2$ and viscosities ${\eta }_1$ and ${\eta }_2$, respectively. They float in eq …

A glass capillary tube is of the shape of a truncated cone with an apex angle $\alpha$ so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height $h$, where the radius of its cross section is $b$. If the surfa …

A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rise …

A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rise …

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance of $1.2m$ from the person. In the following, state of the lift's motion is gi …

A solid sphere of radius $R$ and density $\rho$ is attached to one end of a mass-less spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3\rho$. The complete arrangement is placed in a liquid of den …

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If ${\rho }_c$ is the relative density of the material of the shell with respect to water, then the correct statement is that the sh …

Two solid spheres A and B of equal volumes but of different densities ${\mathrm{d}}_{\mathrm{A}}$ and ${\mathrm{d}}_{\mathrm{B}}$ are connected by a string. They are fully immersed in a fluid of density ${\mathrm{d}}_{\mathrm{F}}$. They get arranged into an equilibrium state as s …

A tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric field of strength $\frac{81\pi }{7}\times 10^5{\mathrm{Vm}}^{-1}$. When the field is switched off, the drop is observed to fall with terminal velocity …

When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at t …

When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at t …

When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at t …

A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice an …

Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure $8\mathrm{N}/{\mathrm{m}}^2$. The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is …

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.
and
STATEMENT-2
In any steady flow of an incompressible fluid, the volume flow rate of the fl …

A small spherical monoatomic ideal gas bubble $\left(\gamma =\frac{5}{3}\right)$ is trapped inside a liquid of density ${\rho }_{\ell }$ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains $n$ moles of gas. The temperature of the …

A small spherical monoatomic ideal gas bubble $\left(\gamma =\frac{5}{3}\right)$ is trapped inside a liquid of density ${\rho }_{\ell }$ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains $n$ moles of gas. The temperature of the …

A small spherical monoatomic ideal gas bubble $\left(\gamma =\frac{5}{3}\right)$ is trapped inside a liquid of density ${\rho }_{\ell }$ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains $n$ moles of gas. The temperature of the …

A glass tube of uniform internal radius $(r)$ has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius $r$. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening t …