Material Deformation and Equilibrium Quiz
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Questions and Answers

What is the strain produced by a hydraulic pressure called?

  • Longitudinal strain
  • Volume strain (correct)
  • Shearing strain
  • Tangential strain

    • What is the strain defined as the ratio of relative displacement of the faces to the length of the cylinder?

  • Tangential strain
  • Volume strain
  • Longitudinal strain
  • Shearing strain (correct)

    • What is the restoring force per unit area developed due to the applied tangential force known as?

  • Shearing stress (correct)
  • Tangential stress
  • Longitudinal stress
  • Hydraulic stress

    • What is the angular displacement of the cylinder from the vertical called?

    <p>Tangential displacement</p> Signup and view all the answers

    What is the strain produced by a shearing force called?

    <p>Shearing strain</p> Signup and view all the answers

    What is the restoring force per unit area developed due to the applied hydraulic pressure known as?

    <p>Hydraulic stress</p> Signup and view all the answers

    What is the ratio of change in volume to the original volume called?

    <p>Volume strain</p> Signup and view all the answers

    What is the strain defined as the ratio of change in dimension to the original dimension?

    <p>Volume strain</p> Signup and view all the answers

    What is the strain produced by the applied tangential force called?

    <p>Shearing strain</p> Signup and view all the answers

    What is the strain produced by a longitudinal force called?

    <p>Longitudinal strain</p> Signup and view all the answers

    What is the restoring force per unit area when a body is stretched by two equal forces applied normal to its cross-sectional area?

    <p>Tensile stress</p> Signup and view all the answers

    What is the SI unit of stress?

    <p>N m$^{-2}$ or pascal (Pa)</p> Signup and view all the answers

    What is the dimensional formula of stress?

    <p>[ ML$^{-1}$T$^{-2}$ ]</p> Signup and view all the answers

    What is the change in the length of a body to the original length when it is subjected to tensile or compressive stress?

    <p>Longitudinal strain</p> Signup and view all the answers

    What is the term for the restoring force per unit area when a cylinder is compressed under the action of applied forces?

    <p>Compressive stress</p> Signup and view all the answers

    In which way does a solid change its dimensions when an external force acts on it in Fig. 8.1(a)?

    <p>Stretched</p> Signup and view all the answers

    What is the restoring force per unit area known as when a body is subjected to tensile or compressive stress?

    <p>Longitudinal stress</p> Signup and view all the answers

    What is the restoring force per unit area when a body is subjected to shearing forces?

    <p>Shear stress</p> Signup and view all the answers

    What is the term for the change in the dimensions of a solid when an external force acts on it?

    <p>Strain</p> Signup and view all the answers

    What is the restoring force per unit area known as when a body is subjected to forces causing change in volume?

    <p>Volumetric stress</p> Signup and view all the answers

    Stress is defined as the restoring force per unit area developed in a body when subjected to deforming forces.

    <p>True</p> Signup and view all the answers

    The SI unit of stress is N m$^{-2}$ or pascal (Pa).

    <p>True</p> Signup and view all the answers

    Longitudinal stress can also be referred to as compressive stress.

    <p>False</p> Signup and view all the answers

    The change in the length of a body to the original length when it is subjected to tensile or compressive stress is known as longitudinal strain.

    <p>True</p> Signup and view all the answers

    The restoring force per unit area developed due to the applied tangential force is known as shear stress.

    <p>True</p> Signup and view all the answers

    The restoring force per unit area developed when a body is stretched by two equal forces applied normal to its cross-sectional area is known as tensile stress.

    <p>True</p> Signup and view all the answers

    The restoring force per unit area when a body is subjected to shearing forces is known as compressive stress.

    <p>False</p> Signup and view all the answers

    The strain produced by the applied tangential force is called lateral strain.

    <p>False</p> Signup and view all the answers

    The change in the length of a cylinder when it is stretched by two equal forces applied normal to its cross-sectional area is known as lateral strain.

    <p>False</p> Signup and view all the answers

    The ratio of change in volume to the original volume is called longitudinal strain.

    <p>False</p> Signup and view all the answers

    Longitudinal strain is defined as the ratio of change in length to the original length of the cylinder.

    <p>False</p> Signup and view all the answers

    When a solid sphere is placed in a fluid under high pressure, it undergoes shearing strain.

    <p>False</p> Signup and view all the answers

    The strain produced by a hydraulic pressure is called volume strain.

    <p>True</p> Signup and view all the answers

    The angular displacement of the cylinder from the vertical is nearly equal to its tangent when the angle is very small.

    <p>True</p> Signup and view all the answers

    The restoring force per unit area developed due to the applied tangential force is known as hydraulic stress.

    <p>False</p> Signup and view all the answers

    The restoring force per unit area developed due to the applied tangential force is known as tangential stress.

    <p>True</p> Signup and view all the answers

    The volume strain has no units or dimensional formula.

    <p>True</p> Signup and view all the answers

    The strain produced by a shearing force is called shearing strain.

    <p>True</p> Signup and view all the answers

    The restoring force per unit area developed due to the applied tangential force is known as tangential stress.

    <p>True</p> Signup and view all the answers

    The restoring force per unit area in the case of hydraulic compression is equal in magnitude to the hydraulic pressure.

    <p>True</p> Signup and view all the answers

    Define stress and give its SI unit and dimensional formula.

    <p>Stress is the restoring force per unit area developed in a body when subjected to deforming forces. Its SI unit is N m$^{-2}$ or pascal (Pa) and its dimensional formula is [ML$^{-1}$T$^{-2}$].</p> Signup and view all the answers

    What are the three ways in which a solid may change its dimensions when an external force acts on it?

    <p>A solid may change its dimensions by stretching (tensile stress), compressing (compressive stress), or undergoing shearing (shearing stress) when an external force acts on it.</p> Signup and view all the answers

    Explain the concept of longitudinal strain.

    <p>Longitudinal strain is the change in the length $\Delta L$ to the original length $L$ of the body when it is subjected to tensile or compressive stress.</p> Signup and view all the answers

    What is the restoring force per unit area known as when a body is subjected to tensile or compressive stress?

    <p>The restoring force per unit area is known as longitudinal stress when a body is subjected to tensile or compressive stress.</p> Signup and view all the answers

    Define the strain produced by a shearing force and give its name.

    <p>The strain produced by a shearing force is called shearing strain, and it is the ratio of the relative displacement of the faces to the length of the body.</p> Signup and view all the answers

    Define shearing strain and provide its mathematical representation.

    <p>Shearing strain is the strain produced by a shearing force and is defined as the ratio of the relative displacement of the faces $\Delta x$ to the length of the cylinder $L$. Mathematically, shearing strain is represented as $\Delta = \frac{\Delta x}{L}$.</p> Signup and view all the answers

    What is volume strain and how is it mathematically expressed?

    <p>Volume strain is the strain produced by a hydraulic pressure and is defined as the ratio of the change in volume $\Delta V$ to the original volume $V$. Mathematically, volume strain is represented as $\Delta = \frac{\Delta V}{V}$.</p> Signup and view all the answers

    Explain the relationship between angle $\theta$ and the tangent of $\theta$ in the context of shearing strain.

    <p>In the context of shearing strain, when the angle $\theta$ is very small, the relationship between $\theta$ and the tangent of $\theta$ can be approximated as $\tan \theta \approx \theta$. This means that if $\theta = 10^\circ$, for example, there is only a 1% difference between $\theta$ and $\tan \theta$.</p> Signup and view all the answers

    What is hydraulic stress and how is it related to the applied hydraulic pressure?

    <p>Hydraulic stress is the internal restoring force per unit area developed in a body when subjected to a hydraulic pressure. Its magnitude is equal to the applied hydraulic pressure (applied force per unit area).</p> Signup and view all the answers

    Explain the concept of longitudinal strain and provide its mathematical expression.

    <p>Longitudinal strain is the strain produced by a longitudinal force and is defined as the ratio of the change in length $\Delta L$ to the original length $L$. Mathematically, longitudinal strain is represented as $\Delta = \frac{\Delta L}{L}$.</p> Signup and view all the answers

    ______ is equal in magnitude but opposite in direction to the applied force

    <p>restoring force</p> Signup and view all the answers

    The SI unit of stress is N m$^{-2}$ or pascal (Pa) and its dimensional formula is

    <p>[ ML$^{-1}$T$^{-2}$ ]</p> Signup and view all the answers

    The restoring force per unit area in this case is called ______ stress

    <p>tensile</p> Signup and view all the answers

    The change in the length ∆L to the original length L of the body is known as ______ strain

    <p>longitudinal</p> Signup and view all the answers

    The restoring force per unit area when a body is subjected to forces causing change in volume is known as ______ stress

    <p>hydraulic</p> Signup and view all the answers

    There are three ways in which a solid may change its dimensions when an external force acts on it. These are shown in Fig. 8.1. In Fig.8.1(a), a cylinder is stretched by two equal forces applied normal to its cross-sectional area. The restoring force per unit area in this case is called ______ stress

    <p>tensile</p> Signup and view all the answers

    The restoring force per unit area when a body is subjected to shearing forces is known as ______ stress

    <p>compressive</p> Signup and view all the answers

    The restoring force per unit area developed due to the applied tangential force is known as ______ stress

    <p>tangential</p> Signup and view all the answers

    The restoring force per unit area developed when a body is stretched by two equal forces applied normal to its cross-sectional area is known as ______ stress

    <p>tensile</p> Signup and view all the answers

    The restoring force per unit area developed due to the applied hydraulic pressure is known as ______ stress

    <p>hydraulic</p> Signup and view all the answers

    Longitudinal strain is defined as the ratio of change in length to the original length of the cylinder.

    <p>longitudinal strain $\Delta = \frac{\Delta L}{L}$</p> Signup and view all the answers

    Shearing strain is defined as the ratio of relative displacement of the faces to the length of the cylinder.

    <p>shearing strain $\Delta = \frac{\Delta x}{L} = \tan \theta$</p> Signup and view all the answers

    The strain produced by a hydraulic pressure is called _____ strain.

    <p>volume</p> Signup and view all the answers

    The restoring force per unit area developed due to the applied tangential force is known as _____ stress.

    <p>tangential or shearing</p> Signup and view all the answers

    The restoring force per unit area in the case of hydraulic compression is equal in magnitude to the hydraulic pressure.

    <p>true</p> Signup and view all the answers

    The angular displacement of the cylinder from the vertical is nearly equal to its tangent when the angle is very small.

    <p>true</p> Signup and view all the answers

    _____ strain has no units or dimensional formula.

    <p>volume</p> Signup and view all the answers

    The restoring force per unit area when a body is stretched by two equal forces applied normal to its cross-sectional area is known as _____ stress.

    <p>tensile</p> Signup and view all the answers

    The restoring force per unit area when a body is subjected to shearing forces is known as _____ stress.

    <p>compressive</p> Signup and view all the answers

    The change in the length of a body to the original length when it is subjected to tensile or compressive stress is known as _____ strain.

    <p>longitudinal</p> Signup and view all the answers

    Match the following terms with their definitions:

    <p>Shearing strain = Ratio of relative displacement of the faces to the length of the cylinder Hydraulic stress = Restoring force per unit area developed due to the applied hydraulic pressure Volume strain = Ratio of change in volume to the original volume Longitudinal strain = Ratio of change in length to the original length of the cylinder</p> Signup and view all the answers

    Match the following stress types with their descriptions:

    <p>Tangential stress = Restoring force per unit area developed due to the applied tangential force Compressive stress = Restoring force per unit area developed when a body is compressed under the action of applied forces Lateral stress = Restoring force per unit area developed when a body is stretched by two equal forces applied normal to its cross-sectional area Hydraulic stress = Restoring force per unit area developed due to the applied hydraulic pressure</p> Signup and view all the answers

    Match the following concepts with their mathematical representations:

    <p>Shearing strain = $\Delta = \frac{\Delta x}{L}$ Volume strain = $\Delta = \frac{\Delta V}{V}$ Longitudinal strain = $\Delta = \frac{\Delta L}{L}$ Tangential stress = Restoring force per unit area developed due to the applied tangential force</p> Signup and view all the answers

    Match the following stress types with their applications:

    <p>Tangential stress = Applied tangential force Compressive stress = Forces causing change in volume Lateral stress = Two equal forces applied normal to the cross-sectional area Hydraulic stress = Fluid under high pressure</p> Signup and view all the answers

    Match the following terms with their examples:

    <p>Shearing strain = Book pressed with the hand and pushed horizontally Hydraulic stress = Solid sphere placed in fluid under high pressure Volume strain = Solid sphere compressed uniformly on all sides Longitudinal strain = Cylinder stretched by two equal forces applied normal to its cross-sectional area</p> Signup and view all the answers

    Study Notes

    Deformation and Stress

    • When a body is subjected to a deforming force, it is deformed to a small or large extent depending on the material and magnitude of the force.
    • The deformation may not be visually noticeable, but it is present.
    • A restoring force is developed in the body, equal in magnitude but opposite in direction to the applied force.

    Stress

    • Stress is the restoring force per unit area.
    • The formula for stress is: Stress = F/A, where F is the force applied normal to the cross-section and A is the area of the cross-section.
    • The SI unit of stress is N m⁻² or Pascal (Pa).
    • The dimensional formula of stress is [ML⁻¹T⁻²].

    Types of Stress

    • There are three ways a solid may change its dimensions when an external force acts on it.
    • Tensile stress occurs when a body is stretched by forces applied normal to its cross-sectional area.
    • Compressive stress occurs when a body is compressed under the action of applied forces.
    • Both tensile and compressive stress can be termed as longitudinal stress.

    Strain

    • Longitudinal strain is the change in length (∆L) to the original length (L) of the body.
    • Longitudinal strain occurs when there is a change in the length of the body due to tensile or compressive stress.

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    Description

    Test your knowledge of material deformation and equilibrium with this quiz. Explore the concepts of deforming forces, restoring forces, and material behavior under external forces.

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