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Stress And Strain - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Stress and it's types is considered one of the most asked concept.

  • 54 Questions around this concept.

Solve by difficulty

Assertion: A piece of metal wire will elongate when subjected to a tensile force.

Reason: When a tensile force is applied to a metal wire, the interatomic spacing between the atoms in the wire increases.

Consider a long steel bar under a tensile force F acting at the edges along the length of the bar. Consider a plane making an angle \Theta with the length. For what angle is the tensile stress is maximum ?

A cable that can support a load w is cut into two equal parts. The maximum load that can be supported by either part is.

Young's modulus of the material of a wire of length L and radius r is Y N/m2. If the length is reduced to \frac{L}{2} and radius to \frac{r}{2} , the Young's modulus will be:-

An elevator cable is to have a maximum stress of 7 \times 10^7 \mathrm{~N} / \mathrm{m}^2 to allow for appropriate safety factors. Its maximum upward acceleration is 1.5 \mathrm{~m} / \mathrm{s}^2. If the cable has to support the total weight of 2000kg of a loaded elevator, the area of the cross-section of the cable should be

One end of a uniform wire of length L and weight W is attached rigidly to a point in the roof and a weight  W_1 is suspended from its lower end. If S is the area of the cross-section of the wire, the stress in the wire at a height of \frac{3L}{4} from its lower end is

A stress of  10^6N/m^2is required for breaking a material. if the density of the material is 3\times 10^3Kg/m^3. What should be the length of the wire made of this material so that it breaks under its own weight.

 

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A force of 20 \mathrm{~N} is applied at one end of a wire of length 2 \mathrm{~m} and having an area of cross-section 10^{-3} \mathrm{~m}^2. The other end of the wire is rigidly fixed. Its coefficient of linear expression of the wire is \alpha=8 \times 10^{-7} /{ }^{\circ} \mathrm{C}, Young's modulus Y=2.2 \times 10^9 \mathrm{~N} / \mathrm{m}^2 and if its temperature is increased by 5^{\circ} \mathrm{C}, then the increase in the tension of the wire will be -

An elevator cable is to have a maximum stress of  7\times 10^{7} N/m^{2} to allow for appropriate safety factors. Its maximum upward acceleration is 1.5 m/s^{2}. If the cable has to support the total weight of 2000 kg of a loaded elevator, the area of cross- section of the cable should be -

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A Uniform Steel bar of cross-sectional area A and length L is suspended so that it hangs vertically. The stress at the middle point of the bar is-

Concepts Covered - 2

Stress and it's types
  • When a force is applied on a body, it is deformed to a small or large extent depending upon the nature of the material of the body and the magnitude of the deforming force.

  • The internal restoring force acting per unit area of cross-section of the deformed body is called stress and is denoted by σ.

  • The magnitude of stress, \sigma =\frac{F}{A}

  • Unit of stress: N/m^2   or Pascal(Pa)

  • Dimension of stress: [ML^{-1}T^{-2}]

  • Types of stress:

  1. Longitudinal stress/ Normal stress: In Longitudinal stress, the force is applied normal to the surface.
  • It is of two types:
  1. Tensile stress: Longitudinal stress produced due to increase in length of a body under a deforming force is called tensile stress.

  2. Compressive stress: Longitudinal stress produced due to decrease in length of a body under a deforming force is called compressional stress.

             

 Fig: Tensile Stress                                                                      Fig: Compressive Stress

  1. Shearing stress/ tangential stress: if two equal and opposite deforming forces are applied parallel to the cross-sectional area of the cylinder, there is a relative displacement between the opposite faces of the cylinder. The restoring force per unit area developed due to the applied tangential force is known as tangential or shearing stress.

  • In this case, deforming force is applied tangential to one of the faces.

  • Area for calculation is the area of the face on which force is applied.

  • It produces change in shape, volume remaining the same.

                                                                                          

Fig:- Shearing stress

       

  1. Volume stress:  

  • It produces change in volume and density, shape remaining the same.

  • It occurs in solids, liquids or gases

  • In case of fluids only bulk stress can be found.

  • It is equal to change in pressure because change in pressure is responsible for change in volume.

Volume \ \ stress= \frac{F}{A}=P

 

 

Strain and it's types
  • Strain is defined as the ratio of change in configuration to the original configuration.

  • It has no dimensions and units as it is the ratio of two similar kind of physical quantities.

  • Types of strain:-

  1. Longitudinal strain:- If the deforming force produces a change in length alone, the strain produced in the body is called longitudinal strain.

  • If the length increases from its natural length, the longitudinal strain is called tensile strain.

  • If the length decreases from its natural length, the longitudinal strain is called compressive strain. 

Longitudinal\ strain=\frac{\Delta L}{L}

                                     

   Fig: Tensile strain         

                               

                                                                                                                                        Fig: Compressive strain

  1. Shear strain:- If the deforming force produces a change in the shape of the body without changing its volume, strain produced is called shearing strain.

  • It is defined as angle in radians through which a plane perpendicular to the fixed surface of the cubical body gets turned under the effect of   tangential force.                 

                                                                 

                                                   

            Fig:- Shearing strain

Shearing \ strain=\frac{\Delta x}{L}

  • Example:- when a book is pressed with the hand and pushed horizontally.

Fig:- A book subjected to a shearing stress       

  1. Volume Strain:- If the deforming force produces a change in volume alone the strain produced in the body is called                                  volumetric strain.

Fig:- Volumetric strain

Volume \ strain=\frac{\Delta V}{V}

 

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Stress and it's types
Strain and it's types

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Reference Books

Stress and it's types

Physics Part II Textbook for Class XI

Page No. : 236

Line : 48

Strain and it's types

Physics Part II Textbook for Class XI

Page No. : 236

Line : 65

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