Mechanical Properties of Fluids

Find the pressure difference of an air bubble of radius 2 cm formed 20 cm below an open water surface and atmospheric pressure.
(Given surface tension of water = \(70\times 1{0}^{−3}\text{ }\text{N/m}\))(Shift - II Memory Based)

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.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of '\(\eta\)' will change.

Choose the correct answer from the options given below:

[JEE Main 2025, 28 Jan (Shift 1)]

Statement 1: Surface tension of soap is greater than water.

Statement 2: Hot water flows faster than cold water.

(Shift I - Memory Based)

A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is \(y\pi \times {10}^{-2}\mathrm{s}\), where the value of \(y\) is
(Acceleration due to gravity, \(g=10\mathrm{m}/{\mathrm{s}}^{2}\), density of water \(={10}^{3}\mathrm{kg}/{\mathrm{m}}^{3}\) )

[JEE Main 2025, 23 Jan (Shift 1)]

A sphere of mass \(M\) is dropped into glycerin. The density of glycerin is half the density of the sphere. After some time, the sphere moves down with constant velocity. What is the viscous force acting on the sphere?

(Shift II Memory Based)​

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density \(1000kg/{m}^{3}\). If the pressure inside the bubble is \(2100N/{m}^{2}\) greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use g\(=10m/{s}^{2}\))

An air bubble at a depth of 20 cm in water has a radius of 1 mm. If the inner pressure of the bubble is greater than the atmospheric pressure by \(2100\mathrm{N}/{\mathrm{m}}^{2}\), find the surface tension of the bubble.

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

[JEE Main 2024, 6 Apr (Shift 2)]

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

Statement 1: Surface tension of soap is greater than water.

Statement 2: Hot water flows faster than cold water.

(Shift I - Memory Based)

A bubble of radius R is split into 27 drops of equal radius, and the work done is 10J. If the same bubble is split into 64 equal drops, the work done is:

(Shift 1 Memory Based)

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density \(1000kg/{m}^{3}\). If the pressure inside the bubble is \(2100N/{m}^{2}\) greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use g\(=10m/{s}^{2}\))

A horizontal pipe of variable cross-section has a fluid of density \(\rho\) flowing through it. At cross-sections A and B, the velocities are \({V}_{A}\)​ and \({V}_{B}\), and the pressures are \({P}_{A}\)​ and \({P}_{B}\)​. Find the correct relation between velocities.

(Shift - II Memory Based)​

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 as acceleration due to gravity)

Consider the following statements:
Statement 1: The surface tension of soap solution is greater than that of water.
Statement 2: Hot water flows faster than cold water.

Which of the following is correct?(shift 1 Memory based)

An air bubble at a depth of 20 cm in water has a radius of 1 mm. If the inner pressure of the bubble is greater than the atmospheric pressure by \(2100\mathrm{N}/{\mathrm{m}}^{2}\), find the surface tension of the bubble.

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 increases, the coefficient of viscosity increases
D. The onset of turbulence is determined by Reynold's number.
E. In a steady flow two stream lines never intersect.

Choose the correct answer from the options given below:

[JEE Main 2025, 28 Jan (Shift 1)]

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

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 \(P_1\). The reading of the pressure gauge falls to \(P_2\) when the valve is opened. The speed of water flowing in the pipe is proportional to

[JEE Main 2025, 23 Jan (Shift 2)]

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 as acceleration due to gravity)

A capillary tube of radius \( r \) is immersed in water and water rises in it to a height \( h \). The mass of the water in the capillary is \( 5 \mathrm{~g} \). Another capillary tube of radius \( 2 r \) is immersed in water. The mass of water that will rise in this tube is:

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 correct answer from the options given below:

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, \(5 \mathrm{~cm}\). 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 liquid \(B\) would be m.

The amount of energy required to form a soap bubble of radius \(2\mathrm{cm}\) from a soap solution is nearly: (surface tension of soap solution \(=0.03\mathrm{N}{\mathrm{m}}^{-1}\) )