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If a piece of material neither expands nor contracts in volume when subjected to stress, then the Poisson‟s ratio must be
- a)Zero
- b)0.25
- c)0.33
- d)0.5
Correct answer is 'D'. Can you explain this answer?
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Verified Answer
If a piece of material neither expands nor contracts in volume when su...
€v=0. (1-2¥)×(£x+£y+£z)/E =0. since body is constrained in all directions there will be equal stress in all directions. £x=£y=£z. 1-2¥=0. ¥=1/2= 0.5 ans.
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If a piece of material neither expands nor contracts in volume when su...
Explanation:
Poisson's ratio is the ratio of lateral strain to longitudinal strain when a material is subjected to stress. It is denoted by the Greek letter nu (ν).
Mathematically, Poisson's ratio can be expressed as:
ν = - (lateral strain) / (longitudinal strain)
where negative sign indicates that lateral strain is opposite in direction to the applied stress.
If a material neither expands nor contracts in volume when subjected to stress, it means that its longitudinal strain is equal to its lateral strain. In other words, the material is incompressible.
Now, let's see how this condition relates to Poisson's ratio:
- When a material is incompressible, its volume remains constant under stress. This means that any increase in the material's lateral dimensions must be accompanied by a decrease in its longitudinal dimension, and vice versa.
- Since the longitudinal strain and lateral strain are equal, their ratio (Poisson's ratio) must be 1. This is because any number divided by itself is 1.
- However, Poisson's ratio is defined as the ratio of lateral strain to longitudinal strain, with a negative sign. Therefore, the Poisson's ratio of an incompressible material is -1, or in other words, 0.5.
Hence, the correct answer is option D, 0.5.
Poisson's ratio is the ratio of lateral strain to longitudinal strain when a material is subjected to stress. It is denoted by the Greek letter nu (ν).
Mathematically, Poisson's ratio can be expressed as:
ν = - (lateral strain) / (longitudinal strain)
where negative sign indicates that lateral strain is opposite in direction to the applied stress.
If a material neither expands nor contracts in volume when subjected to stress, it means that its longitudinal strain is equal to its lateral strain. In other words, the material is incompressible.
Now, let's see how this condition relates to Poisson's ratio:
- When a material is incompressible, its volume remains constant under stress. This means that any increase in the material's lateral dimensions must be accompanied by a decrease in its longitudinal dimension, and vice versa.
- Since the longitudinal strain and lateral strain are equal, their ratio (Poisson's ratio) must be 1. This is because any number divided by itself is 1.
- However, Poisson's ratio is defined as the ratio of lateral strain to longitudinal strain, with a negative sign. Therefore, the Poisson's ratio of an incompressible material is -1, or in other words, 0.5.
Hence, the correct answer is option D, 0.5.
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Community Answer
If a piece of material neither expands nor contracts in volume when su...
€v=0. (1-2¥)×(£x+£y+£z)/E =0. since body is constrained in all directions there will be equal stress in all directions. £x=£y=£z. 1-2¥=0. ¥=1/2=.5 ans.
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If a piece of material neither expands nor contracts in volume when subjected to stress, then the Poisson‟s ratio must bea)Zerob)0.25c)0.33d)0.5Correct answer is 'D'. Can you explain this answer?
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