When an elastic body is subjected to an axial tensile force, it undergoes: 

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  1. decrease in length and increase in cross-sectional area
  2. increase in length and increase in cross-sectional area 
  3. increase in length and decrease in cross-sectional area
  4. decrease in length and decrease in cross-sectional area 

Answer (Detailed Solution Below)

Option 3 : increase in length and decrease in cross-sectional area
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Detailed Solution

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Explanation:

When an elastic body is subjected to a tensile axial force, it experiences elongation along the direction of the force. This results in the following effects:

1. Increase in Length (Axial Elongation):

  • The tensile force pulls the material, causing it to stretch in the direction of the applied force.

  • This is the primary deformation experienced by the body.

2. Decrease in Cross-Sectional Area (Lateral Contraction):

  • While the length increases, the cross-sectional area reduces due to conservation of volume (approximately) in elastic materials.

Additional InformationElastic Body

  • An elastic body is a material that returns to its original shape and size after the removal of the load, provided the stress is within its elastic limit.

  • Follows Hooke's Law, where stress is directly proportional to strain within the elastic range.

  • Examples: mild steel, aluminum (in elastic range), rubber (though highly elastic, not linearly).

 Strain

  • Axial strain: Change in length per unit original length.

  • Lateral strain: Change in cross-sectional dimension per unit original dimension.

  • These strains help in analyzing how materials deform under load.

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