Mechanical Engineering Exam > Mechanical Engineering Questions > If a piece of material neither expands nor co...
Start Learning for Free
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?
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.
Most Upvoted Answer
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.
Free Test
FREE
| Start Free Test |
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.
|
Explore Courses for Mechanical Engineering exam
|
|
Top Courses for Mechanical EngineeringView all
Question Description
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? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 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? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 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? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
Solutions for 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? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution for 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup