Properties Of Solids And Liquids PYQs

Match List I with List II: Choose the correct answer from the options given below:

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)

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity 2K while that in the middle has thermal conductivity K. The left end of the combination is maintained at temperature 3T and the right end at T. The rods are thermally insulated from outside. In steady state, the temperature at the left junction is $T_1$ and that at the right junction is $T_2$. The ratio $T_1$/$T_2$ is

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

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young modulus, respectively, are 8 × 10⁸ N m⁻² and 2 × 10¹¹ N m⁻², is:

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:

A metallic bar of Young’s modulus 0.5 × 10¹¹ N m⁻² and coefficient of linear expansion 10⁻⁵ °C⁻¹, length 1 m and area of cross-section 10⁻³ m² is heated from 0°C to 100°C without expansion or bending. The compressive force developed in it 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]

An object kept in a large room having air temperature of 25°C takes 12 minutes to cool from 80°C to 70°C. The time taken to cool for the same object from 70°C to 60°C would be nearly:

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:

The stress-strain curves are drawn for two different materials X and Y. It is observed that the ultimate strength point and the fracture point are close to each other for material X but are far apart for material Y. We can say that materials X and Y are likely to be (respectively),

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:

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δl on applying a force F, how much force is needed to stretch the second wire by the same amount?

The bulk modulus of a spherical object is $B$. If it is subjected to uniform pressure $p$, then the fractional decrease in radius is:

Two rods $A$ and $B$ of different materials are welded together as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be:

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:

Copper of fixed volume 'V; is drawn into a wire of length 'l'. When this wire is subjected to a constant force 'F', the extension produced in the wire is '$\Delta$l'. Which of the following graphs is a straight line?

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

The two ends of a rod of length $L$ and uniform cross-sectional area $A$ are kept at temperatures $T_1$ and $T_2$ ($T_1>T_2$). The rate of heat transfer dQ/dt through the rod in steady state is:

A black body at $227^{\circ}C$ radiates heat at the rate of $7\,\mathrm{cal\,cm^{-2}s^{-1}}$. At $727^{\circ}C$, the rate of heat radiated will be:

If the lattice parameter for a crystalline structure is 3.6 Å, then the atomic radius in fcc crystal is

Which of the following circular rods, each made of the same material and whose ends are maintained at the same temperature difference, will conduct most heat?