Mechanical Properties of Fluids PYQs

A submarine is designed to withstand an absolute pressure of 100 atm. How deep can it go below the water surface? (Consider density of water = 1000 kg m⁻³, 1 atm = 1 × 10⁵ Pa and gravitational acceleration g = 10 m/s²)

Consider a water tank shown in the figure. It has one wall at x = L and can be taken to be very wide in the z direction. When filled with a liquid of surface tension S and density ρ, the liquid surface makes angle θ₀ (θ₀ << 1) with the x-axis at x = L. If y(x) is the height of the surface then the equation for y(x) is : (take θ(x) = sin θ(x) = tan θ(x) = dy/dx, g is the acceleration due to gravity)

A balloon is made of a material of surface tension $S$ and its inflation outlet (from where gas is filled in it) has small area $A$. It is filled with a gas of density $\rho$ and takes a spherical shape of radius $R$. When the gas is allowed to flow freely out of it, its radius $r$ changes from $R$ to $0$ (zero) in time $T$. If the speed $v(r)$ of gas coming out of the balloon depends on $r$ as $r^a$ and $T \propto S^\alpha A^\beta \rho^\gamma R^\delta$, then

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

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 venturi-meter works on :

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

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

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

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 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is:

In a U-tube as shown in the figure, water and oil are in the left side and right side of the tube respectively. The heights from the bottom for water and oil columns are 15 cm and 20 cm respectively. The density of the oil is [take ρ₍water₎ = 1000 kg/m³]

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

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

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 $10\ \text{mm}$ above the water level on the other side. Meanwhile the water rises by $65\ \text{mm}$ from its original level (see diagram). The density of the oil is

A rectangular film of liquid is extended from $(4\ \text{cm} \times 2\ \text{cm})$ to $(5\ \text{cm} \times 4\ \text{cm})$. If the work done is $3 \times 10^{-4}\ \text{J}$, the value of surface tension of the liquid is:

Three liquids of densities $\rho_1$, $\rho_2$ and $\rho_3$ (with $\rho_1 > \rho_2 > \rho_3$), having the same value of surface tension $T$, rise to the same height in three identical capillaries. The angles of contact $\theta_1$, $\theta_2$ and $\theta_3$ obey:

The cylindrical tube of a spray pump has radius $R$, one end of which has fine holes, each of radius $r$. If the speed of the liquid in the tube is $V$, the speed of ejection of the liquid through the holes is:

The heart of a man pumps $5$ litres of blood through the arteries per minute at a pressure of $150\,\text{mm}$ of mercury. If the density of mercury is $13.6\times10^3\,\text{kg/m}^{3}$ and $g=10\,\text{m/s}^{2}$, then the power of heart in watt is:

Water rises to height $h$ in a capillary tube. If the length of capillary tube above the surface of water is made less than $h$, then:

A certain number of spherical drops of a liquid of radius 'r' coalesce to form a single drop of radius 'R' and volume 'V'. If 'T' is the surface tension of the liquid, then:

The wettability of a surface by a liquid depends primarily on