Properties of Bulk Matter Questions and Answers

Answer: B

With rising temperature, both T and η decrease.

Surface tension comes from cohesive forces between molecules at the surface. As temperature rises the molecules move faster and these forces weaken, so surface tension falls, becoming zero at the critical temperature.

The viscosity of a liquid also comes mainly from intermolecular attraction between layers. Heating loosens that attraction, so a liquid's viscosity decreases markedly with temperature, which is why warm honey or oil pours more easily. The trap is the behaviour of gases, whose viscosity increases with temperature; that is not the case for a liquid, so the options in which η rises are wrong.

Answer: E

The speed of efflux is \(\sqrt{2gh}\), Torricelli's law.

Apply Bernoulli's equation between the free surface and the opening. Both are at atmospheric pressure, and in a large tank the surface barely moves, so its speed is taken as zero:

\[ \begin{aligned} P_{a} + \rho g h &= P_{a} + \tfrac{1}{2}\rho v^{2} \\ v &= \sqrt{2gh} \end{aligned} \]

This is the speed a body would gain falling freely through height h. \(\sqrt{gh}\) and \(\sqrt{4gh}\) have the wrong factor. \(gh\) and \(2gh\) have units of speed squared (m² s^-2), so they cannot be a speed at all.

Answer: A

The material is ductile.

Between the ultimate (maximum) stress and the fracture point, a material undergoes large plastic deformation, drawing out and necking before it breaks. When these two points are far apart, the material can be stretched a great deal plastically, which is ductility, as in copper or mild steel.

A brittle material fractures soon after the ultimate stress, so the two points are close together. 'Perfectly elastic' would show no plastic region at all, and hardness and malleability are separate properties.

Answer: E

The gauge pressure is \(P - P_{a}\).

Absolute pressure at depth h is \(P = P_{a} + \rho gh\). Gauge pressure is the excess over atmospheric pressure, the part a pressure gauge open to the air reads.

\[ P_{gauge} = P - P_{a} = \rho gh \]

\(P + P_{a}\) double-counts the atmosphere, and the halved or doubled forms have no physical meaning here.

Answer: C

The answer is venturimeter, that is, the Venturi (Bernoulli) effect on which the venturimeter works.

In a Bunsen burner, gas leaves a narrow jet at high speed. By Bernoulli's principle, the fast-moving stream has low pressure, so air is drawn in through the side holes and mixes with the gas before it burns. This is the same pressure drop at a constriction that a venturimeter uses to measure flow.

Pascal's law is about pressure transmitted through a fluid at rest (the hydraulic press), the law of flotation and Archimedes' principle are about buoyancy, and Torricelli's law gives the speed of efflux from a hole in a tank.

Answer: A

Bernoulli's principle applies to non-viscous, incompressible fluids in streamline flow.

The principle is energy conservation along a streamline: \(P + \frac{1}{2}\rho v^{2} + \rho gh\) stays constant. Its derivation assumes no energy is lost to viscous friction, the density is constant, and the flow is steady along streamlines.

Viscosity dissipates energy, compressibility changes the density, and turbulent flow has no fixed streamlines, so every option containing viscous, compressible or turbulent breaks one of these assumptions.

Answer: B

The pressure increases with depth.

The pressure at depth h in a liquid of density \(\rho\) is \(P = P_{0} + h\rho g\), which grows linearly with h because more liquid lies above the point.

It depends only on the depth, not on the shape of the container (the hydrostatic paradox), and it is not zero or constant.

Answer: C

The angle of contact is the angle between the tangent to the liquid surface and the solid surface within the liquid, at the point of contact.

It is measured inside the liquid. It is acute for liquids that wet the solid (water on clean glass, a concave meniscus) and obtuse for those that do not (mercury on glass, a convex meniscus).

The other options leave out the tangent, measure the angle outside the liquid, or refer to normals or centres of curvature, none of which is the definition.

Answer: D

The speed in the narrow section is 12 m/s.

By the equation of continuity, \(A_{1}v_{1} = A_{2}v_{2}\). Halving the diameter makes the area a quarter, so the speed becomes four times:

\[ \begin{aligned} v_{2} &= v_{1}\frac{A_{1}}{A_{2}} \\ &= 3 \times 4 \\ &= 12\ \text{m/s} \end{aligned} \]

The pressure is not needed. 6 m/s assumes the speed scales with the diameter instead of the area, and 24 m/s doubles that again.

The given pressure is a distractor for this part; it would be needed only to find the pressure in the narrow section with Bernoulli's equation.

Answer: D

The pressure energy per unit mass is \(\frac{P}{\rho}\).

Pushing a volume \(dV\) of liquid against pressure \(P\) takes work \(P\,dV\); that is its pressure energy. The mass of that volume is \(\rho\,dV\), so per unit mass:

\[ \frac{P\,dV}{\rho\,dV} = \frac{P}{\rho} \]

This is the \(\frac{P}{\rho}\) term in Bernoulli's equation written per unit mass. \(P\,dV\) is the energy of the whole volume, not per unit mass, and \(\frac{P\,dV}{\rho}\) leaves an extra volume factor. \(P\rho\) has the wrong units.