Fluid Mechanics — JEE Main PYQs

The area of cross-section of a large tank is $0.5{\text{m}}^2$. It has a narrow opening near the bottom having area of cross-section $1{\text{cm}}^2$. A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity o …

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Clothes containing oil or grease stains cannot be cleaned by water wash.
Reason (R) : Because the angle of contact between the oil/ grease and water is obtus …

The terminal velocity ( ${\mathrm{v}}_{\mathrm{t}}$ ) of the spherical rain drop depends on the radius ( $r$ ) of the spherical rain drop as:-

The velocity of upper layer of water in a river is $36{\mathrm{kmh}}^{-1}$. Shearing stress between horizontal layers of water is $10^{-3}{\mathrm{Nm}}^{-2}$. Depth of the river is ______ m. (Co-efficiency of viscosity of water is $10^{-2}Pa.s$)

Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube.
[Take surface tension of water …

A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ______ cm.

A hydraulic press can lift 100 kg when a mass '$m$' is placed on the smaller piston. It can lift ______ kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass '$m$' on the smaller piston.

Two small drops of mercury each of radius R coalesce to from a single large drop. The ratio of total surface energy before and after the change is :

A large number of water drops, each of radius $r$, combine to have a drop of radius $R$. If the surface tension is T and mechanical equivalent of heat is J , the rise in heat energy per unit volume will be:

A balloon carries a total load of 185 kg at normal pressure and temperature of $27^{\circ }\mathrm{C}$. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is $-7^{\circ }\mathrm{C}$?

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 $\times 10^{-5}\mathrm{m}$ and density $1.2\times 10^3{\mathrm{kgm}}^{-3}$ ? Take viscosity of liquid $=1.8\times 10^{-5}{\mathrm{Nsm}}^{-2}$. (Neglect buoyancy due to air …

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is …

When two soap bubbles of radii a and $\mathrm{b}(\mathrm{b}>\mathrm{a})$ coalesce, the radius of curvature of common surface is:

Two spherical soap bubbles of radii $r_1$ and $r_2$ in vacuum combine under isothermal conditions. The resulting bubble has radius equal to :

A raindrop with radius $\mathrm{R}=0.2\mathrm{mm}$ falls from a cloud at a heighth $=2000\mathrm{m}$ above the ground. Assume that the drop is spherical through its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is :
[Density …

The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth ' $h$ ' below the water level. The value of ' $h$ ' for which the emerging stream of water strikes the ground at the maximum range is ____ m.

The pressure acting on a submarine is $3\times 10^5\mathrm{Pa}$ at a certain depth. If the depth is doubled, the percentage in the pressure acting on the submarine would be: (Assume that atmospheric pressure is $1\times 10^5\mathrm{Pa}$ density of water is …

What will be the nature of flow of water form a circular tap, when its flow rate increased from $0.18\mathrm{L}/\min$ to $0.48\mathrm{L}/\min$ ? The radius of the tap and viscosity of water are 0.5 cm and $10^{-3}\mathrm{Pa}\mathrm{s}$, respectively.
( …

Consider a water tank as shown in the figure. Its cross-sectional area is $0.4{\mathrm{m}}^2$. The tank has an opening B near the bottom whose cross-sectional area is $1{\mathrm{cm}}^2$. A load of 24 kg is applied on the water at the top when the height of the water level …

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is

Consider a solid sphere of radius $R$ and mass density $p(r)=p_0\left(1-\frac{r^2}{R^2}\right),0<r\le R$. The minimum density of a liquid in which it will float is

A leak proof cylinder of length 1 m , made of a metal which has very low coefficient of expansion is floating vertically in water at $0^{\circ }\mathrm{C}$ such that its height above the water surface is 20 cm . When the temperature of water is increased to …

Two liquids of densities ${\rho }_1$ and ${\rho }_2$ (${\rho }_2=2{\rho }_1$) are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (A …

A small spherical droplet of density $d$ is floating exactly half immersed in a liquid of density $\rho$ and surface tension T . The radius of the droplet is (take note that the surface tension applies an upward force on the droplet):

Water flows in a horizontal tube (see figure). The pressure of water changes by $700{\text{ Nm}}^{-2}$ between A and B where the area of cross section are $40{\text{ cm}}^2$ and $20{\text{ cm}}^2$, respectively. Find the rate of flow of water through the tube. (density of water …

In an experiment to verify Stokes law, a small spherical ball of radius $r$ and density $\rho$ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water …

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is

When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to $0^{\circ }$, the surface tension of the liquid, in milli Newton ${\mathrm{m}}^{-1}$, is …

A fluid is flowing through a horizontal pipe of varying cross-section, with speed $\mathrm{v}{\mathrm{ms}}^{-1}$ a ta point where the pressure is P Pascal. At another point where pressure is $\frac{\mathrm{P}}{2}$ Pascal its speed is $\mathrm{V}{\mathrm{ms}}^{-1}$. If the density o …

A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is $r$. If the specific gravity of the shell material is $\frac{27}{8}$ w.r.t water, the value of $r$ is.

A air bubble of radius 1 cm in water has an upward acceleration $9.8\mathrm{cm}{\mathrm{s}}^{-2}$. The density of water is $1\mathrm{gm}{\mathrm{cm}}^{-3}$ and water offers negligible drag force on the bubble. The mass of the bubble is: …

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is $x_1$ and in the other, $x_2$. When both cylinders are connected through a pipe of n …

Water from a pipe is coming at a rate of 100 litres per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of: (density of water = 1000 $\mathrm{kg}/{\mathrm{m}}^3$, coefficient of viscosity of water $=1\mathrm{mPa}\mathrm{s}$)

If ' M ' is the mass of water that rises in a capillary tube of radius ' $r$ ', then mass of water which will rise in a capillary tube of radius ' $2r$ ' is:

Water flows into a large tank with flat bottom at the rate of $10^{-4}{\mathrm{m}}^3{\mathrm{s}}^{-1}$. Water is also leaking out of a hole of area $1{\mathrm{cm}}^2$ at its bottom. If the height of the water in the tank remains steady, then this height is:

Water from a tap emerges vertically downwards with an initial speed of $1.0{\mathrm{ms}}^{-1}$. The cross-sectional area of the tap is $10^{-4}{\mathrm{m}}^2$. Assume that the pressure is constant throughout the stream of water and that flow is streamlined. The cross-sectional …

A submarine experiences a pressure of $5.05\times 10^6\mathrm{Pa}$ at a depth of ${\mathrm{d}}_1$ in a sea. When it goes further to a depth of $d_2$, it experiences a pressure of $8.08\times 10^6\mathrm{Pa}$. Then $d_2-d_1$ is approximately (density of water …

A cubical block of side 0.5 m floats on water with $30\%$ of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water?
[Take density of water $=10^3\mathrm{kg}/{\mathrm{m}}^3$]

A solid sphere, of radius R acquires a terminal velocity $v_1$ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $\eta$. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, …

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the ce …

A wooden block floating in a bucket of water has $\frac{4}{5}$ of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relati …

The top of a water tank is open to air and its water level is maintained. It is giving out $0.74{\mathrm{m}}^3$ water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:

The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6 . Their contact angles, with glass, are close to $135^{\circ }$ and $0^{\circ }$, respectively. It is observed that mercury gets depressed by an amount $h$ in a capillar …

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities ${\mathrm{d}}_1$ and ${\mathrm{d}}_2$ are filled in the tube. Each liquid subtends $90^{\circ }$ angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical. ratio …

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius $r$ with the bottom of the vessel. If $r\ll R$, and the surface tension of water is T, value of r just before bu …

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring …

Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T , density of liquid is $\rho$ and L is its latent heat of vapori …

A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5\times 10^{-2}\mathrm{N}$ (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is

Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly (Surface tension of soap solution $=0.03{\text{ Nm}}^{-1}$) :

Water is flowing continuously from a tap having an internal diameter $8\times 10^{-3}\mathrm{m}$. The water velocity as it leaves the tap is $0.4{\mathrm{ms}}^{-1}$. The diameter of the water stream at a distance $2\times 10^{-1}\mathrm{m}$ below the lap is close to :