Mechanical Properties Of Fluids

Two non-mixing liquids of densities ρ and nρ (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p < 1) in the denser liquid. The density d is equal to:

A rectangular film of liquid is extended from (4 cm × 2 cm) to (5 cm × 4 cm). If the work done is 3 × 10⁻⁴ J, the value of the surface tension of the liquid is:

Three liquids of densities ρ₁, ρ₂ and ρ₃ (with ρ₁ > ρ₂ > ρ₃), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact θ₁, θ₂ and θ₃ obey:

A U-tube with both ends open to the atmosphere is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see figure). The density of the oil is:

A small sphere of radius 'r' falls from rest in a viscous liquid. As a result, heat is produced due to the viscous force. The rate of production of heat, when the sphere attains its terminal velocity, is proportional to:

A small hole of cross-sectional area 2 mm² is present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m s⁻², the rate of flow of water through the open hole would be nearly:

A soap bubble of radius 1 mm is blown from a detergent solution of surface tension 2.5 × 10⁻² N m⁻¹. The pressure inside the bubble equals the pressure at a point Z₀ below the free surface of water in a container. Taking g = 10 m s⁻² and density of water = 10³ kg m⁻³, the value of Z₀ is:

Two small spherical metal balls of equal mass are made from materials of densities ρ₁ and ρ₂ (ρ₁ = 8ρ₂) and have radii 1 mm and 2 mm respectively. They fall vertically from rest in a viscous medium of coefficient of viscosity η and density 0.1ρ₂. The ratio of their terminal velocities is:

In a U-tube, water and oil are in the left and right arms respectively. The heights of the water and oil columns (measured from the bottom) are 15 cm and 20 cm respectively. The density of the oil is: (take ρ_water = 1000 kg m⁻³)

The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is d/2, then the viscous force acting on the ball will be:

A spherical ball is dropped in a long column of a highly viscous liquid. Which curve in the graph shown represents the speed of the ball (v) as a function of time (t)?

If a soap bubble expands, the pressure inside the bubble:

The venturi-meter works on:

The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly: (surface tension of soap solution = 0.03 N m⁻¹)

The viscous drag acting on a metal sphere of diameter 1 mm, falling through a fluid of viscosity 0.8 Pa·s with a velocity of 2 m s⁻¹, is equal to:

A simple pendulum oscillating in air has a period of √3 s. If it is completely immersed in a non-viscous liquid having density 1/4 th of the material of the bob, the new period will be:

A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If the surface tension of water is 0.07 N m⁻¹, then the excess force required to take it away from the surface is:

A balloon is made of a material of surface tension S and its inflation outlet (from where gas is filled) has small area A. It is filled with a gas of density ρ and takes a spherical shape of radius R. When the gas flows freely out, its radius r changes from R to 0 in time T. If the speed v(r) of gas coming out depends on r as rᵅ and T ∝ Sᵝ Aᵞ Rᵟ ρᵋ, then:

Consider a water tank with one wall at x = L, very wide in the z-direction. When filled with a liquid of surface tension S and density ρ, the liquid surface makes a small angle θ₀ (0 < θ₀ ≪ 1) with the x-axis at x = L. If y(x) is the height of the surface, the equation for y(x) is: (take sinθ(x) ≈ tanθ(x) = dy/dx, g = acceleration due to gravity)

Water flows in streamline motion through a horizontal pipe of circular cross-section as shown. The pressure difference of water between $P$ and $Q$ is $15\,\text{Nm}^{-2}$. The areas of cross-section at $P$ and $Q$ are $40\,\text{cm}^2$ and $20\,\text{cm}^2$ respectively. The rate of flow of water through the pipe (in $\text{cm}^3\text{s}^{-1}$) is: [density of water $=1000\,\text{kg m}^{-3}$]

A submarine is designed to withstand an absolute pressure of 100 atm. How deep can it go below the water surface? (density of water = 1000 kg m⁻³, 1 atm = 1 × 10⁵ Pa, g = 10 m s⁻²)

In the measurement of viscosity of liquids using the terminal velocity experiment, spherical balls of the same radius but different densities are used. The variation of the terminal velocity $v$ with the ratio of the density of the spherical ball ($\sigma$) to the density of the liquid ($\rho$), $\sigma/\rho$, is best represented by: