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A rod of length 20mm is stretched to make a rod of length 40 mm. Subsequently, it is compressed to make a rod of final length 10 mm. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is_______
  • a)
    -0.5
  • b)
    -0.69
  • c)
    -0.75
  • d)
    -1
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A rod of length 20mm is stretched to make a rod of length 40 mm. Subse...
< b="" />Given data:
- Initial length of the rod (L1) = 20 mm
- Final length of the rod after stretching (L2) = 40 mm
- Final length of the rod after compression (L3) = 10 mm

Calculation:
1. Calculating the tensile strain when the rod is stretched:
Tensile strain (ε1) = (Change in length)/(Original length)
ε1 = (L2 - L1) / L1
ε1 = (40 - 20) / 20
ε1 = 20 / 20
ε1 = 1
2. Calculating the compressive strain when the rod is compressed:
Compressive strain (ε2) = (Change in length)/(Original length)
ε2 = (L3 - L2) / L2
ε2 = (10 - 40) / 40
ε2 = -30 / 40
ε2 = -0.75
3. Total true longitudinal strain in the rod:
Total strain = ε1 + ε2
Total strain = 1 + (-0.75)
Total strain = 0.25
Therefore, the total true longitudinal strain in the rod is -0.75.
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Community Answer
A rod of length 20mm is stretched to make a rod of length 40 mm. Subse...
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