JEE Properties of Fluids PYQs with Video Solutions PDF

A large liquid drop of radius $$R$$ and surface tension $$\sigma$$ is placed on a smooth horizontal surface. A tiny pin is used to pierce the drop, causing it to instantly split into $$N$$ identical smaller droplets. During this  process, surface energy of the system increases. If the entire change in surface energy is given to  the collective kinetic energy of the expanding cloud of new droplets, the initial outward speed $$v$$ of each droplet of mass $$m$$ immediately after the split is given by:

A horizontal pipe has a non-uniform cross-section. The velocity of water at a point where the radius is $$2r$$ is found to be $$v$$. The velocity of water at another point in the same pipe where the radius is $$r$$ will be:

Two wires $$A$$ and $$B$$ of the same material have lengths in the ratio $$1:2$$ and diameters in the ratio $$2:1$$. If both wires are subjected to the same stretching force, the ratio of the elongation produced in wire $$A$$ to that in wire $$B$$ ($$\Delta L_A : \Delta L_B$$) will be:

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 center and the sides, in cm, will be:

A small spherical ball of radius 0.1 mm and density $$10^4$$ kg m$$^{-3}$$ falls freely under gravity through 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 constant velocity inside water, then the value of $$h$$ will be ______ m. (Given $$g = 10$$ m s$$^{-2}$$, viscosity of water $$= 1.0 \times 10^{-5}$$ N-s m$$^{-2}$$).

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 $$T = 7.3 \times 10^{-2}$$ N m$$^{-1}$$, angle of contact = 0, $$g = 10$$ m s$$^{-2}$$ and density of water = $$1.0 \times 10^3$$ kg m$$^{-3}$$]

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of 0.8 cm$$^3$$. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was _____ litre. (Take 1 atm = $$10^5$$ Pa)

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):

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

A certain pressure 'P' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0.01% whereas the liquid gets compressed to 0.03%. The ratio of Bulk modulus of water to that of the liquid is $$\frac{3}{x}$$. The value of $$x$$ is _____.

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?

A U- tube whose ends are open and whose limbs are vertical, contains oil of specific gravity 0.8 and surface tension 28 dynes/cm. If one limb has a diameter of 2.2 mm and other of 0.8mm, difference in level of oil in the two limbs is: (contact angle = 0)

A cube (edge length $$L$$) of specific gravity $$"n"$$ is suspended from a thin metal wire. The fundamental frequency for transverse standing waves in the wire is $$f_0$$. When the same cube is partially immersed in a liquid of specific gravity $$2$$ up to a depth of $$h$$, the new fundamental frequency will be

An incompressible liquid flows steadily through a horizontal pipe of non-uniform cross-section. If the radius of the pipe at a point where the velocity of flow is $$2 \,\, \text{m/s}$$ is $$4 \,\, \text{cm}$$, then the velocity of flow at another point where the radius of the pipe is $$2 \,\, \text{cm}$$ will be:

A spherical liquid drop of radius $$R$$ acquires the terminal velocity $$v_1$$ when falls through a gas of viscosity $$\eta$$. Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity $$v_2$$ falling through the same gas. The ratio of terminal velocities $$v_1/v_2$$ is __________.

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 range of water falling on the ground in the beginning is __________ cm.

If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter $$\frac{2}{\sqrt{\pi}}$$ cm then the Reynolds number for the flow is (density of water = $$10^3$$ kg/m$$^3$$ and viscosity of water = $$10^{-3}$$ Pa.s) close to:

The velocity of water in a river is 18 km h$$^{-1}$$ near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water = $$10^{-2}$$ poise.

Wax is coated on the inner wall of a capillary tube and the tube is then dipped in water. Then, compared to the unwaxed capillary, the angle of contact $$\theta$$ and the height $$h$$ upto which water rises change. These changes are :

The bulk moduli of ethanol, mercury and water are given as 0.9, 25 and 2.2 respectively in units of $$10^9$$ Nm$$^{-2}$$. For a given value of pressure, the fractional compression in volume is $$\frac{\Delta V}{V}$$. Which of the following statements about $$\frac{\Delta V}{V}$$ for these three liquids is correct?

Water is flowing at a speed of 1.5 m s$$^{-1}$$ through a horizontal tube of cross-sectional area $$10^{-2}$$ m$$^2$$ and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water = $$10^3$$ kg m$$^{-3}$$)

A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 N m$$^{-1}$$, density = 667 kg m$$^{-3}$$) which rises to height h in the tube. It is observed that the two tangents drawn from observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60$$°$$ with one another. Then h is close to (g = 10 m s$$^{-2}$$):

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 $$5 \times 10^5$$ N is applied on the top surface of water using a piston. The speed of efflux from the hole will be: (given atmospheric pressure $$P_A = 1.01 \times 10^5$$ Pa, density of water $$\rho_w = 1000$$ kg m$$^{-3}$$ and gravitational acceleration $$g = 10 \ m s^{-2}$$)

Water from a tap emerges vertically downwards with an initial speed of 1.0 ms$$^{-1}$$. The cross-sectional area of the tap is $$10^{-4}$$ m$$^2$$. Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross-sectional area of the stream, 0.15 m below the tap would be:
(Take g = 10 ms$$^{-2}$$)

A liquid of density 750 kg m$$^{-3}$$ flows smoothly through a horizontal pipe that tapers in cross-sectional area from $$A_1 = 1.2 \times 10^{-2}$$ m$$^2$$ to $$A_2 = \frac{A_1}{2}$$. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ______ $$\times 10^{-3}$$ m$$^3$$ s$$^{-1}$$.

The pressure acting on a submarine is $$3 \times 10^5$$ Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be: (Assume that atmospheric pressure is $$1 \times 10^5$$ Pa, density of water is $$10^3$$ kg m$$^{-3}$$, g = 10 ms$$^{-2}$$)

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

Water flows in a horizontal tube (see figure). The pressure of water changes by $$700 \; Nm^{-2}$$ between $$A$$ and $$B$$ where the area of cross section are $$40 \; cm^2$$ and $$20 \; cm^2$$, respectively. Find the rate of flow of water through the tube. (density of water $$= 1000 \; kgm^{-3}$$)

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:

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° and 0°, respectively. If it is observed that mercury gets depressed by an amount $$h$$ in a capillary tube of radius $$r_1$$, while water rises by the same amount $$h$$ in a capillary tube of radius $$r_2$$, then the ratio $$\frac{r_1}{r_2}$$ is close to

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$$^3$$ kg/m$$^3$$]

A submarine experiences a pressure of $$5.05 \times 10^6$$ Pa at a depth of d$$_1$$ in a sea. When it goes further to a depth of d$$_2$$, it experiences a pressure of $$8.08 \times 10^6$$ Pa. Then d$$_2$$ - d$$_1$$ is approximately (density of water = 10$$^3$$ kg/m$$^3$$ and acceleration due to gravity = 10 ms$$^{-2}$$):