Properties of Bulk Matter

Breaking stress of a wire depends on:

The ratio of change in dimension to the original dimension is:

Which of the following is NOT a type of stress?

What is the nature of the stress-strain graph within the proportional limit?

Two wires of equal length $L$ and the same cross-sectional area $A$ are joined end-to-end (in series) to form a composite wire of total length $2L$. The Young's moduli of the materials of the two wires are $Y_1$ and $Y_2$ respectively. When a longitudinal force $F$ is applied to the end of the composite wire, the effective Young's modulus $Y$ of the entire system is given by:

When a force is applied to a wire, the potential energy stored in it is $U$. If the force is doubled (within elastic limit), the potential energy stored becomes:

Which modulus is most relevant for calculating the change in volume of a solid sphere under high pressure at the bottom of the ocean?

When a force is applied to a wire, it extends by $0.01\%$. If the Young's modulus is $10^{11}\text{ N/m}^2$, the energy stored per unit volume is:

A metallic ring of radius $R$ and cross-sectional area $A$ is fitted onto a wooden cylinder of radius $R + \Delta R$. If the Young's modulus of the metal is $Y$, the tension in the ring is:

A load of $4.0\text{ kg}$ is suspended from a ceiling through a steel wire of length $2.0\text{ m}$ and radius $2.0\text{ mm}$. It is found that the length of the wire increases by $0.031\text{ mm}$ at equilibrium. Find the Young's modulus of steel ($g = 3.1 \pi\text{ m/s}^2$ for calculation ease).

The pressure at a point in a fluid at rest depends on the:

Which property of mercury makes it suitable for use in a barometer?

What is the pressure at a depth where the water pressure is equal to $2$ atmospheres (excluding $P_{atm}$)?

The variation of pressure $P$ with depth $h$ in a liquid is:

A hydraulic system is based on the principle that pressure is transmitted equally in all directions. This is known as:

A sample of an alloy weighing $500\ gf$ in air weighs $450\ gf$ in water. What is its relative density?

A barometer tube is tilted at an angle of $30^\circ$ with the vertical. The length of the mercury column along the tube will:

A piece of alloy of mass $50\ g$ and density $5\ g/cm^3$ is immersed in a liquid of density $1.2\ g/cm^3$. What is the apparent weight of the alloy in the liquid?

A cylindrical tank of height $H$ is completely filled with a liquid of density $\rho$. The ratio of the force exerted by the liquid on the base to the force exerted on the vertical wall is:

A large vessel is filled with water. A small wooden block is floating on the surface. If the vessel is allowed to fall freely under gravity, the buoyant force on the block becomes:

If a sphere of radius $R$ has a terminal velocity $V$, what is the terminal velocity of a sphere of radius $R/2$ made of the same material in the same liquid?

If the temperature of a gas is increased, its viscosity increases because:

Which of the following units is equivalent to $N \cdot s \cdot m^{-2}$?

Viscosity is often compared to friction. How is it different from solid friction?

A sphere of mass $M$ and radius $R$ is falling in a viscous fluid. At terminal velocity, the rate of work done by the gravitational force is:

The coefficient of viscosity of a liquid is a measure of:

For a sphere falling in a viscous medium, the terminal velocity is attained when:

A ball of mass $m$ and radius $r$ is falling through a liquid. The viscous force is $F = 6\pi \eta r v$. The terminal velocity is reached when:

Two spheres $X$ and $Y$ have radii $r$ and $2r$ and are made of materials with densities $\rho$ and $2\rho$ respectively. They fall in the same viscous liquid. The ratio of their terminal velocities $v_X/v_Y$ is (neglecting liquid density $\sigma$):

A spherical ball falls through a viscous medium with terminal velocity $v$. If the radius of the ball is $R$, the drag force $F$ is proportional to $R$. This means that the power dissipated by the drag force at terminal velocity is proportional to:

Which of the following is the correct unit for energy per unit volume?

In the equation $P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$, the term $P$ is called:

A Pitot tube is an instrument used to measure:

If the velocity of a liquid flowing in a horizontal pipe is doubled, the 'velocity head' becomes:

Which of the following is the correct expression for Bernoulli's theorem per unit weight?

In an ideal fluid flow, the 'head' that depends on the reference level chosen is:

The Bernoulli's equation is derived by integrating:

A wind with speed $40\text{ m/s}$ blows parallel to the roof of a house. The area of the roof is $250\text{ m}^2$. Assuming the pressure inside the house is atmospheric pressure, what is the net force exerted by the wind on the roof? ($Density of air = 1.2\text{ kg/m}^3$)

A liquid is filled in a container up to height $H$. A small hole is made at height $h$ from the bottom. The time taken for the liquid jet to reach the ground is $t$. If $g$ is the acceleration due to gravity, then $t$ is:

An ideal fluid flows through a vertical pipe that tapers downwards. At the top (radius $R$, height $H$), the velocity is $v$. At the bottom (radius $r$, height $0$), the pressure is the same as at the top. Find $v$ in terms of $R, r, g, H$.

According to the molecular theory of surface tension, the behavior of a liquid surface is explained by the resultant cohesive forces acting on its molecules. Based on the provided diagram, which of the following correctly describes the net cohesive force acting on molecule A (located deep in the bulk) and molecule B (located on the surface)?

What is the angle of contact for mercury with a glass surface?

The force required to lift a horizontal thin wire loop of radius $r$ from a liquid surface with surface tension $T$ is (neglecting weight):

The molecules in the surface film of a liquid possess:

Two parallel glass plates are dipped vertically into water. The separation between the plates is $d$ and the surface tension of water is $T$. The rise of water between the plates is:

If the surface tension of water is $0.072 \text{ N/m}$, the energy required to increase the surface area of a water film by $0.01 \text{ m}^2$ is:

When the temperature increases, the intermolecular distance increases, which causes the surface tension to:

If the temperature of a liquid is increased, the surface tension generally:

A soap bubble $A$ of radius $r$ and another bubble $B$ of radius $2r$ are brought together so that they have a common interface. The radius of the interface is:

Two glass plates are separated by a thin layer of water of thickness $t$. If the area of the plates in contact with water is $A$ and surface tension is $T$, the force required to pull them apart is: