1. A substance is described as a fluid in mechanics mainly because it can
ⓐ. keep a fixed shape under all forces
ⓑ. resist every change in volume completely
ⓒ. support static tangential stress like a rigid body
ⓓ. flow and take the shape of its container
Correct Answer: flow and take the shape of its container
Explanation: A fluid is a substance that can flow, so it does not keep a fixed shape like a solid. Liquids and gases are both treated as fluids because their parts can move relative to one another. A liquid may have nearly fixed volume, but its shape changes according to the vessel. A gas can change both shape and volume much more easily. The key idea is flow, not whether the substance is heavy, transparent, or wet.
2. In fluid mechanics, liquids and gases are grouped together because both
ⓐ. have fixed volume and fixed shape
ⓑ. have no weight in a container
ⓒ. always have the same density
ⓓ. can flow under applied forces
Correct Answer: can flow under applied forces
Explanation: Liquids and gases are classified as fluids because both can flow. A liquid has nearly fixed volume but no fixed shape, while a gas has neither fixed shape nor fixed volume under ordinary conditions. Both differ from solids because a solid can maintain its shape under small applied forces. Fluids adjust their shape according to the boundaries around them. The shared property is their ability to flow, not equality of density or volume.
3. Pressure is introduced in fluid mechanics as
ⓐ. force acting parallel to a surface per unit length
ⓑ. normal force acting per unit area
ⓒ. mass contained in unit volume
ⓓ. volume of fluid crossing a section per second
Correct Answer: normal force acting per unit area
Explanation: Pressure measures how much normal force acts on a unit area of a surface. Its basic relation is \(P=\frac{F}{A}\), where \(F\) is the normal force and \(A\) is the area. The word normal is important because pressure on a surface acts perpendicular to that surface. Mass per unit volume describes density, not pressure. Volume crossing a section per second describes flow rate, so it belongs to fluid motion rather than the definition of pressure.
4. The SI unit of pressure is completed by the relation \(1\,\text{Pa}=1\,\_\_\_\_\).
ⓐ. \(\text{N m}^{-1}\)
ⓑ. \(\text{N m}^{-2}\)
ⓒ. \(\text{kg m}^{-3}\)
ⓓ. \(\text{m s}^{-1}\)
Correct Answer: \(\text{N m}^{-2}\)
Explanation: Pressure is force per unit area, so its unit comes from \(\frac{\text{N}}{\text{m}^2}\). Therefore, \(1\,\text{Pa}=1\,\text{N m}^{-2}\). The unit \(\text{N m}^{-1}\) is force per unit length and is used for quantities such as surface tension. The unit \(\text{kg m}^{-3}\) belongs to density, while \(\text{m s}^{-1}\) belongs to speed. The exponent \(-2\) on metre reminds us that pressure depends on area, not length.
5. Density of a fluid sample is best described by
ⓐ. \(\rho=\frac{V}{m}\)
ⓑ. \(\rho=mV\)
ⓒ. \(\rho=\frac{m}{V}\)
ⓓ. \(\rho=\frac{F}{A}\)
Correct Answer: \(\rho=\frac{m}{V}\)
Explanation: Density tells how much mass is contained in unit volume. Its defining relation is \(\rho=\frac{m}{V}\), where \(m\) is mass and \(V\) is volume. The reciprocal \(\frac{V}{m}\) does not represent density. The relation \(\frac{F}{A}\) gives pressure, so it belongs to force distribution over area. Density later becomes important in hydrostatic pressure and buoyancy because heavier fluids for the same volume produce larger effects.
6. A \(2.0\,\text{kg}\) liquid sample occupies \(2.5\times10^{-3}\,\text{m}^3\). What is its density?
ⓐ. \(5.0\times10^{-3}\,\text{kg m}^{-3}\)
ⓑ. \(8.0\times10^{2}\,\text{kg m}^{-3}\)
ⓒ. \(1.25\times10^{-3}\,\text{kg m}^{-3}\)
ⓓ. \(4.5\times10^{2}\,\text{kg m}^{-3}\)
Correct Answer: \(8.0\times10^{2}\,\text{kg m}^{-3}\)
Explanation: \( \textbf{Given:} \) \(m=2.0\,\text{kg}\) and \(V=2.5\times10^{-3}\,\text{m}^3\).
\( \textbf{Required:} \) Density \(\rho\).
\( \textbf{Relation used:} \)
\[
\rho=\frac{m}{V}
\]
This relation applies because density is mass per unit volume.
\( \textbf{Substitution:} \)
\[
\rho=\frac{2.0}{2.5\times10^{-3}}
\]
\( \textbf{Calculation:} \)
\[
\rho=\frac{2.0}{0.0025}=800\,\text{kg m}^{-3}
\]
\( \textbf{Final answer:} \) The density is \(8.0\times10^{2}\,\text{kg m}^{-3}\).
7. Match the basic quantities with their SI units.
| Quantity | SI unit |
|---|
| P. Pressure | 1. \(\text{kg m}^{-3}\) |
| Q. Force | 2. \(\text{m}^2\) |
| R. Area | 3. \(\text{N}\) |
| S. Density | 4. \(\text{Pa}\) |
ⓐ. P-3, Q-4, R-1, S-2
ⓑ. P-1, Q-3, R-2, S-4
ⓒ. P-4, Q-2, R-3, S-1
ⓓ. P-4, Q-3, R-2, S-1
Correct Answer: P-4, Q-3, R-2, S-1
Explanation: Pressure is measured in pascal, written as \(\text{Pa}\). Force is measured in newton, written as \(\text{N}\). Area is measured in square metre, \(\text{m}^2\), because it involves two length dimensions. Density is mass per unit volume, so its SI unit is \(\text{kg m}^{-3}\). The unit pairing is also supported by \(P=\frac{F}{A}\), which gives \(\text{N m}^{-2}\) for pressure.
8. A liquid and a gas are compared in ordinary conditions. The better comparison is that
ⓐ. a gas has fixed shape, while a liquid has fixed shape only at high pressure
ⓑ. a liquid has nearly fixed volume, while a gas is highly compressible
ⓒ. both liquids and gases have fixed shape but not fixed volume
ⓓ. a liquid is always compressible, while a gas is always incompressible
Correct Answer: a liquid has nearly fixed volume, while a gas is highly compressible
Explanation: Liquids and gases are both fluids, but they do not behave identically. A liquid has nearly fixed volume because its particles are relatively close together. A gas is much more compressible because its particles are far apart and the volume can change greatly under pressure. Neither liquid nor gas has a fixed shape like a solid. The distinction matters because many fluid formulas treat liquids as nearly incompressible, while gases often require more care.
9. Use the arrangement described below.
A beaker, a closed gas jar, a wooden block, and a stream of water from a tap are placed on a table. The beaker contains water, the gas jar contains air, and the wooden block keeps its own shape.
Which pair should be classified as fluids?
ⓐ. Air and wooden block
ⓑ. Water and air
ⓒ. Wooden block and water only when water freezes
ⓓ. Beaker and wooden block
Correct Answer: Water and air
Explanation: Water is a liquid and air is a gas, so both are fluids. They can flow and can take the shape of the space available to them. The wooden block is a solid because it keeps its shape under ordinary conditions. The beaker is only a container, not the fluid being studied. A fluid need not be visible as a stream; even still air in a jar is a fluid because it can flow when allowed to move.
10. A pressure of \(600\,\text{Pa}\) acts uniformly on an area of \(0.20\,\text{m}^2\). What normal force is acting on the area?
ⓐ. \(3000\,\text{N}\)
ⓑ. \(600.2\,\text{N}\)
ⓒ. \(120\,\text{N}\)
ⓓ. \(60\,\text{N}\)
Correct Answer: \(120\,\text{N}\)
Explanation: \( \textbf{Given:} \) \(P=600\,\text{Pa}=600\,\text{N m}^{-2}\) and \(A=0.20\,\text{m}^2\).
\( \textbf{Required:} \) Normal force \(F\).
\( \textbf{Pressure relation:} \)
\[
P=\frac{F}{A}
\]
Rearranging gives:
\[
F=PA
\]
\( \textbf{Substitution:} \)
\[
F=(600)(0.20)
\]
\( \textbf{Calculation:} \)
\[
F=120\,\text{N}
\]
\( \textbf{Unit check:} \) \(\text{N m}^{-2}\times\text{m}^2=\text{N}\), so the result is a force.
\( \textbf{Final answer:} \) The normal force is \(120\,\text{N}\).
11. A sealed plastic bottle is completely filled with water and then gently pressed from outside. For many simple fluid-mechanics discussions, water inside the bottle is treated as nearly incompressible because
ⓐ. its density changes noticeably with pressure
ⓑ. it cannot transmit pressure to the walls
ⓒ. it behaves like a rigid solid with fixed shape
ⓓ. its volume changes very little under pressure
Correct Answer: its volume changes very little under pressure
Explanation: An incompressible-fluid approximation means that the fluid volume is taken as nearly constant. Liquids such as water usually change volume very little under ordinary pressure changes, so this approximation is useful in many problems. This does not mean that water has a fixed shape like a solid. Water still flows and takes the shape of the container. The approximation is about volume change, not about the ability to exert pressure or flow.
12. Consider the following statements about the symbols used at the start of fluid mechanics.
Statement I: \(P\) commonly denotes pressure.
Statement II: \(\rho\) commonly denotes density.
Statement III: \(v\) commonly denotes the speed of fluid flow.
ⓐ. I and II only
ⓑ. II and III only
ⓒ. I, II and III
ⓓ. I and III only
Correct Answer: I, II and III
Explanation: The symbol \(P\) is commonly used for pressure in fluid mechanics. The symbol \(\rho\) represents density, especially in relations such as \(\rho=\frac{m}{V}\) and later in hydrostatic pressure. The symbol \(v\) often represents speed of fluid flow. These symbols are used across pressure, buoyancy, continuity, and Bernoulli relations. Keeping the symbols clear prevents mixing up pressure \(P\), density \(\rho\), and flow speed \(v\).
13. A claim says: “A larger force always means a larger pressure.” The best response is that the claim is incomplete because pressure also depends on
ⓐ. magnitude of the force alone
ⓑ. contact area
ⓒ. shape of the container only
ⓓ. time for which the force acts
Correct Answer: contact area
Explanation: Pressure is not decided by force alone. From \(P=\frac{F}{A}\), pressure increases when the same force acts on a smaller area and decreases when it acts on a larger area. A large force spread over a very large area may produce smaller pressure than a smaller force concentrated on a tiny area. This is why pressure is more specific than just thrust or normal force. The area in the denominator is the missing part of the claim.
14. Study the table and identify the row that gives the most suitable first meaning.
| Row | Term | Meaning |
|---|
| P | Density | Normal force per unit area |
| Q | Pressure | Mass per unit volume |
| R | Buoyancy | Upward force exerted by a fluid on an immersed body |
| S | Flow rate | Weight of fluid per unit area |
ⓐ. Row P
ⓑ. Row Q
ⓒ. Row S
ⓓ. Row R
Correct Answer: Row R
Explanation: Buoyancy is the upward force exerted by a fluid on a body partly or completely immersed in it. Row P swaps density with pressure, because density is mass per unit volume. Row Q also reverses the meanings of pressure and density. Flow rate is related to volume of fluid crossing a section per unit time, not weight per unit area. The upward nature of buoyancy is the first feature to remember before using Archimedes’ principle later.
15. Read the situation and answer the question.
A small wooden piece is placed gently on the surface of water. It does not sink to the bottom. The water pushes the wooden piece upward while gravity pulls it downward.
In this situation, the upward push of water is called
ⓐ. viscous drag only
ⓑ. surface pressure only
ⓒ. buoyant force
ⓓ. volume flow rate
Correct Answer: buoyant force
Explanation: The upward push exerted by a fluid on an immersed or floating body is called buoyant force. In this case, water pushes upward on the wooden piece while gravity acts downward. For a floating body at rest, these two effects balance in the vertical direction. Viscous drag is related to resistance during relative motion through a fluid, which is not the main idea here. Buoyancy is introduced through the direction of the force before its full formula is developed.
16. A short note says that \(Q\) in elementary fluid flow represents the volume of fluid crossing a section per unit time. Its SI unit should be
ⓐ. \(\text{m}^3/\text{s}\)
ⓑ. \(\text{m}/\text{s}\)
ⓒ. \(\text{kg}/\text{m}^3\)
ⓓ. \(\text{N}/\text{m}^2\)
Correct Answer: \(\text{m}^3/\text{s}\)
Explanation: Volume flow rate or discharge is volume per unit time. The SI unit of volume is \(\text{m}^3\), and the SI unit of time is \(\text{s}\). Therefore, the unit of \(Q\) is \(\text{m}^3\text{s}^{-1}\). The unit \(\text{m s}^{-1}\) belongs to speed, while \(\text{kg m}^{-3}\) belongs to density. The notation \(Q\) should not be confused with force or pressure, because it describes how quickly fluid volume crosses an area.
17. In a simple description of surface tension, the free surface of a liquid behaves somewhat like
ⓐ. a rigid metal plate
ⓑ. a vacuum region with no molecules
ⓒ. a source of gravitational force only
ⓓ. a stretched membrane
Correct Answer: a stretched membrane
Explanation: Surface tension is a surface effect of liquids. It makes the free surface behave as if it were a stretched membrane under tension. This idea helps explain why small drops tend to become nearly spherical and why some light objects can rest carefully on a liquid surface. The surface is not actually a rigid plate, because the liquid can still flow and change shape. The stretched-membrane model gives the first physical picture before force-per-length and surface-energy relations are used later.
18. A beginner writes four symbol-unit pairs for fluid mechanics. Select the pair that is not suitable.
ⓐ. \(A\) with \(\text{m}^2\)
ⓑ. \(v\) with \(\text{m s}^{-1}\)
ⓒ. \(\rho\) with \(\text{kg m}^{-3}\)
ⓓ. \(P\) with \(\text{kg m}^{-3}\)
Correct Answer: \(P\) with \(\text{kg m}^{-3}\)
Explanation: The symbol \(P\) denotes pressure, whose SI unit is \(\text{Pa}\) or \(\text{N m}^{-2}\). The unit \(\text{kg m}^{-3}\) belongs to density \(\rho\), not pressure. Area \(A\) is measured in \(\text{m}^2\), and speed \(v\) is measured in \(\text{m s}^{-1}\). This distinction is important because later formulas combine these quantities, such as \(\rho gh\), \(Av\), and \(P=\frac{F}{A}\). A wrong unit usually signals that two different physical quantities have been mixed.
19. Relative density compares the density of a substance with the density of
ⓐ. air at room temperature
ⓑ. mercury in a barometer
ⓒ. water as reference
ⓓ. the same substance in gaseous form
Correct Answer: water as reference
Explanation: Relative density is the ratio of the density of a substance to the density of water taken as reference. Since it is a ratio of two densities, it has no unit. A substance with relative density greater than \(1\) is denser than water, while a value less than \(1\) means it is less dense than water. This idea is useful when comparing floating and sinking behaviour in fluids. The comparison is with water, not with air or mercury.
20. A fluid is treated as incompressible in a simple calculation when its
ⓐ. density changes greatly during the process
ⓑ. flow speed is fixed by definition
ⓒ. pressure remains the same everywhere
ⓓ. density remains nearly constant
Correct Answer: density remains nearly constant
Explanation: An incompressible fluid is one whose volume, and therefore density, changes very little under the conditions being studied. Many liquid-flow calculations use this approximation because liquids such as water are only slightly compressible in ordinary situations. This does not mean pressure is zero; pressure can still vary with depth or applied force. It also does not require the fluid to be at rest. The approximation mainly keeps \(\rho\) nearly constant in relations involving pressure, buoyancy, and flow.
