1. Mechanical properties of solids mainly describe how a solid behaves when an external force tries to deform it. What is the most suitable description of this idea?
ⓐ. How a solid changes its chemical composition when heated
ⓑ. How a solid deforms under force and recovers
ⓒ. How a solid conducts electric current through free electrons
ⓓ. How a solid reflects light from its surface
Correct Answer: How a solid deforms under force and recovers
Explanation: Mechanical properties of solids deal with the response of a solid body to applied forces. The important response here is deformation, meaning a change in shape or size. The chapter also studies whether the body regains its original form after the force is removed. This makes the topic different from thermal, electrical, or optical properties. A stretched wire, compressed spring, or bent ruler is more relevant here than a heated or electrically conducting solid.
2. A thin metal ruler is held at one end and gently bent at the other end. In this situation, the word deformation refers to the ruler's change in
ⓐ. colour only
ⓑ. temperature only
ⓒ. shape or size
ⓓ. mass only
Correct Answer: shape or size
Explanation: Deformation means a change in the shape, size, or both of a body due to an applied force. In the bent ruler, the shape changes even if the mass and material remain the same. The change may be small or large depending on the force and the material. Deformation does not require a change in colour or temperature. A body can be deformed even when its chemical identity and mass are unchanged.
3. A rubber band is stretched gently and then released. It almost returns to its original length. This behaviour is best described as
ⓐ. plasticity
ⓑ. fracture
ⓒ. elasticity
ⓓ. melting
Correct Answer: elasticity
Explanation: Elasticity is the ability of a body to regain its original shape and size after the deforming force is removed. In the rubber band example, the band is first deformed by stretching and then recovers when released. The recovery need not be perfectly ideal in every real material, but the tendency to return is the elastic behaviour. Plasticity would mean retaining a permanent deformation after the force is removed. Melting and fracture describe different physical changes, not ordinary recovery after deformation.
4. A piece of clay is pressed into a new shape and it keeps that shape after the hand is removed. The behaviour shown by the clay is mainly
ⓐ. elastic behaviour
ⓑ. plastic behaviour
ⓒ. oscillatory behaviour
ⓓ. magnetic behaviour
Correct Answer: plastic behaviour
Explanation: Plastic behaviour means the body does not fully regain its original shape after the deforming force is removed. Clay and putty are common examples because they can retain the shape given to them. The applied force changes the arrangement of the material in a way that leaves a permanent set. Elastic behaviour would require the body to return close to its original shape. This question separates temporary deformation from permanent deformation.
5. In a loaded wire, the hanging weight acts on the wire and produces elongation. The force responsible for producing the deformation is called the
ⓐ. restoring force
ⓑ. deforming force
ⓒ. frictional force
ⓓ. buoyant force
Correct Answer: deforming force
Explanation: A deforming force is an external force that changes the shape or size of a body. In a loaded wire, the weight pulls the wire and tends to increase its length. The restoring force is different; it is developed inside the solid and opposes the deformation. Friction and buoyancy are not the central forces in this stretched-wire situation. The same external force can produce different deformations in different bodies because material response also matters.
6. When a spring is stretched slightly and held at rest, an internal force develops in the spring. This internal force mainly acts to
ⓐ. help the deformation continue increasing
ⓑ. restore the spring's original length
ⓒ. change the mass of the spring
ⓓ. turn the spring into a liquid
Correct Answer: restore the spring's original length
Explanation: The restoring force is an internal force that develops in a deformed body. It acts opposite to the deformation and tends to bring the body back to its original shape or size. In a stretched spring, this force pulls the spring back toward its natural length. The applied external force and the internal restoring force may balance when the spring is held at rest. This restoring tendency is closely connected with the elasticity of the solid.
7. The table gives some basic quantities used while describing deformation of a solid.
| Quantity | Meaning |
|---|
| P | \(F\) |
| Q | \(A\) |
| R | \(L\) |
| S | \(\Delta L\) |
Which matching is most appropriate for the symbols?
ⓐ. \(P\): pressure, \(Q\): acceleration, \(R\): load, \(S\): volume
ⓑ. \(P\): area, \(Q\): force, \(R\): change in volume, \(S\): original length
ⓒ. \(P\): strain, \(Q\): stress, \(R\): modulus, \(S\): density
ⓓ. \(P\): force, \(Q\): area, \(R\): original length, \(S\): change in length
Correct Answer: \(P\): force, \(Q\): area, \(R\): original length, \(S\): change in length
Explanation: In the usual notation of elasticity, \(F\) represents force and \(A\) represents cross-sectional area. The symbol \(L\) commonly denotes the original length of a wire or rod. The symbol \(\Delta L\) denotes the change in length, such as extension or compression. These symbols prepare the formulas for stress, strain, and Young's modulus. Confusing \(L\) with \(\Delta L\) later leads to a wrong strain calculation.
8. In SI units, stress is measured in ______.
ⓐ. \( \text{N} \)
ⓑ. \( \text{m} \)
ⓒ. \( \text{Pa} \)
ⓓ. \( \text{kg} \)
Correct Answer: \( \text{Pa} \)
Explanation: Stress is force per unit area, so its unit comes from force divided by area. The SI unit of force is \( \text{N} \), and the SI unit of area is \( \text{m}^2 \). Therefore, the SI unit of stress is \( \text{N m}^{-2} \), which is also called \( \text{Pa} \). A force alone has unit \( \text{N} \), but stress must include the area over which the force acts. The unit \( \text{Pa} \) is shared by pressure and stress because both are force per unit area.
9. A wire of original length \(L\) increases in length by \(\Delta L\). The quantity \(\frac{\Delta L}{L}\) represents
ⓐ. force
ⓑ. stress
ⓒ. longitudinal strain
ⓓ. cross-sectional area
Correct Answer: longitudinal strain
Explanation: Longitudinal strain is the fractional change in length of a body. It is defined as the change in length divided by the original length, so the expression is \(\frac{\Delta L}{L}\). The numerator \(\Delta L\) alone is only extension, not strain. Stress involves force and area, not change in length divided by length. Using the original length in the denominator is essential because the same extension can be a small or large strain depending on the initial length.
10. A learner writes that strain has unit \( \text{m} \) because extension is measured in \( \text{m} \). What is the best correction?
ⓐ. Strain has unit \( \text{N} \) because force causes deformation
ⓑ. Strain has unit \( \text{Pa} \) because it is related to stress
ⓒ. Strain is dimensionless because like quantities are compared
ⓓ. Strain has unit \( \text{m}^2 \) because area affects deformation
Correct Answer: Strain is dimensionless because like quantities are compared
Explanation: Strain is not the same as extension. For longitudinal strain, the definition is \(\frac{\Delta L}{L}\), where both \(\Delta L\) and \(L\) are measured in \( \text{m} \). The units cancel because a length is divided by a length. Therefore, strain is dimensionless and has no SI unit. This distinction matters because extension depends on the size of the object, while strain compares the change with the original size.
11. A wire of length \(2.0\,\text{m}\) is stretched so that its length increases by \(1.0\,\text{mm}\). What is its longitudinal strain?
ⓐ. \(2.0\times10^{-3}\)
ⓑ. \(5.0\times10^{-4}\)
ⓒ. \(1.0\times10^{-3}\)
ⓓ. \(5.0\times10^{-3}\)
Correct Answer: \(5.0\times10^{-4}\)
Explanation: \( \textbf{Known data:} \) Original length \(L=2.0\,\text{m}\).
Extension \(\Delta L=1.0\,\text{mm}\).
Convert the extension into metres:
\[\Delta L=1.0\times10^{-3}\,\text{m}\]
\( \textbf{Required quantity:} \) Longitudinal strain.
The suitable relation is:
\[\epsilon_L=\frac{\Delta L}{L}\]
This relation applies because longitudinal strain compares the change in length with the original length.
Substituting the values:
\[\epsilon_L=\frac{1.0\times10^{-3}}{2.0}\]
\[\epsilon_L=5.0\times10^{-4}\]
Strain has no unit because \( \text{m} \) cancels with \( \text{m} \).
\( \textbf{Final answer:} \) \(5.0\times10^{-4}\).
12. Two wires are made of the same material, but one is long and thin while the other is short and thick. When equal loads are applied, their extensions may be different mainly because
ⓐ. deformation depends only on the name of the material
ⓑ. extension depends on both dimensions and material
ⓒ. a solid cannot develop restoring force
ⓓ. strain must always be equal to extension
Correct Answer: extension depends on both dimensions and material
Explanation: The response of a solid body depends on both the material and the object's dimensions. A long, thin wire generally stretches more easily than a short, thick wire of the same material under the same load. The material property describes how the substance resists deformation, but the actual extension also depends on length and area. This is why object response and material property should not be treated as identical. Strain is also not the same as extension because strain is a fractional change.
13. A block is pressed uniformly from all sides so that its shape remains almost the same but its volume decreases slightly. This is mainly a case of
ⓐ. change in colour
ⓑ. change in electric charge
ⓒ. change in mass
ⓓ. change in size
Correct Answer: change in size
Explanation: Uniform pressure from all sides mainly changes the volume of a body. The shape can remain nearly similar while the size decreases. This is different from shearing, where the shape changes without a major change in volume. It is also different from stretching a wire, where the length changes prominently. The example prepares the idea that deformation may be a change in length, volume, or shape depending on how the force is applied.
14. A force of \(20\,\text{N}\) acts normally on an area of \(4.0\,\text{m}^2\). The stress produced is
ⓐ. \(16\,\text{Pa}\)
ⓑ. \(24\,\text{Pa}\)
ⓒ. \(80\,\text{Pa}\)
ⓓ. \(5.0\,\text{Pa}\)
Correct Answer: \(5.0\,\text{Pa}\)
Explanation: \( \textbf{Known data:} \) Force \(F=20\,\text{N}\).
Area \(A=4.0\,\text{m}^2\).
\( \textbf{Required quantity:} \) Stress \(\sigma\).
Stress is force per unit area:
\[\sigma=\frac{F}{A}\]
This relation is used because the force is distributed over the given area.
Substituting:
\[\sigma=\frac{20}{4.0}\,\text{N m}^{-2}\]
\[\sigma=5.0\,\text{N m}^{-2}\]
Since \(1\,\text{N m}^{-2}=1\,\text{Pa}\), the stress is \(5.0\,\text{Pa}\).
\( \textbf{Final answer:} \) \(5.0\,\text{Pa}\).
15. The same force is applied normally to two flat surfaces. Surface P has area \(A\), while surface Q has area \(2A\). Compared with the stress on P, the stress on Q is
ⓐ. twice as large
ⓑ. half as large
ⓒ. the same
ⓓ. four times as large
Correct Answer: half as large
Explanation: Stress depends on both force and area. The relation is \(\sigma=\frac{F}{A}\). If the force remains the same but the area becomes \(2A\), the stress becomes \(\frac{F}{2A}\). This is half of the stress on the smaller area \(A\). The result shows why stress is not just another name for force; the area over which the force acts is equally important.
16. A rectangular eraser is pushed sideways on its top face while its bottom face is held fixed. The top face shifts slightly, but the volume changes very little. The deformation is best described as
ⓐ. purely volumetric deformation
ⓑ. melting of the eraser
ⓒ. change only in mass
ⓓ. shearing type deformation
Correct Answer: shearing type deformation
Explanation: In this arrangement, the force is tangential to the face of the body. The main effect is a change in shape because one layer shifts relative to another. The volume does not need to change appreciably for shearing deformation. This is different from uniform compression, where the main change is in volume. The fixed-bottom and shifted-top description is the standard starting picture for shear in solids.
17. In a simple material comparison, material P undergoes less strain than material Q under the same stress in the elastic range. The better basic conclusion is that material P has
ⓐ. smaller stiffness
ⓑ. larger stiffness
ⓒ. no restoring force
ⓓ. no deformation at all
Correct Answer: larger stiffness
Explanation: A material that produces less strain under the same stress resists deformation more strongly. In the elastic range, the ratio of stress to strain is related to elastic modulus. A larger modulus means the material is stiffer, not that it is impossible to deform. The phrase “less strain” does not mean zero deformation; it means smaller fractional deformation. This distinction helps avoid confusing stiffness with perfect rigidity.
18. A short record of observations is given below.
| Case | Observation after removing the force |
|---|
| P | A stretched steel spring nearly returns to its original length |
| Q | A pressed lump of putty keeps its new shape |
| R | A bent ruler springs back when the bending force is small |
Which classification is most suitable?
ⓐ. \(P\) plastic, \(Q\) elastic, \(R\) plastic
ⓑ. \(P\) elastic, \(Q\) elastic, \(R\) plastic
ⓒ. \(P\) elastic, \(Q\) plastic, \(R\) elastic
ⓓ. \(P\) plastic, \(Q\) plastic, \(R\) elastic
Correct Answer: \(P\) elastic, \(Q\) plastic, \(R\) elastic
Explanation: Elastic behaviour is identified by recovery after the deforming force is removed. The steel spring and the gently bent ruler show this recovery, so cases \(P\) and \(R\) are elastic in the stated conditions. Plastic behaviour is identified by permanent deformation after the force is removed. The putty keeps its new shape, so case \(Q\) is plastic. The same object may not remain elastic for every possible force, so the condition “small” is meaningful for the bent ruler.
19. A wire carrying a suspended load is held at rest after a small extension. At that instant, the internal restoring force in the wire is best described as
ⓐ. zero because the wire has stopped moving
ⓑ. a force that balances the load and acts oppositely
ⓒ. greater than the load in the same direction
ⓓ. unrelated to the deformation of the wire
Correct Answer: a force that balances the load and acts oppositely
Explanation: When the loaded wire is at rest, the forces on it are balanced. The external load acts as a deforming force and produces extension. The wire develops an internal restoring force that opposes this extension. In static equilibrium, this restoring force has the same magnitude as the applied load but acts in the opposite direction. The absence of motion does not mean absence of force; it means the opposing forces balance each other.
20. A spring returns to its original length after a small load is removed, but it remains slightly longer after a much larger load is removed. This observation mainly shows that
ⓐ. restoring force is always zero in a spring
ⓑ. plastic deformation occurs before any deformation begins
ⓒ. recovery is limited by the elastic range
ⓓ. stress is independent of the applied force
Correct Answer: recovery is limited by the elastic range
Explanation: Real elastic bodies usually show nearly complete recovery only within a certain range of applied force or stress. For a small load, the spring can regain its original length because the deformation remains within the elastic range. For a much larger load, the spring may cross the range where complete recovery is possible and retain a permanent extension. This permanent extension indicates plastic deformation. Elasticity is not the same as unlimited recovery under every possible load.
