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If x, y and z are the reciprocal of the Young's modulus of elasticity, modulus of rigidity and bulk modulus of elasticity respectively, the correct correlation is,
- a)x = (3y + z)/9
- b)x = (9y +z)/9
- c)x = (y + 3z)/9
- d)x = (3y + 2z)/9
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If x, y and z are the reciprocal of the Youngs modulus of elasticity, ...
E = Young's modulus of elasticity
C = modulus of rigidity
K = bulk modulus of elasticity
x = 1/E
y = 1/C
z = 1/ K
C = modulus of rigidity
K = bulk modulus of elasticity
x = 1/E
y = 1/C
z = 1/ K
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Community Answer
If x, y and z are the reciprocal of the Youngs modulus of elasticity, ...
Understanding Elastic Moduli
The question revolves around the relationships between three fundamental material properties: Young's modulus of elasticity (E), modulus of rigidity (G), and bulk modulus of elasticity (K). Their reciprocals are defined as:
- \( x = \frac{1}{E} \) (Reciprocal of Young's modulus)
- \( y = \frac{1}{G} \) (Reciprocal of modulus of rigidity)
- \( z = \frac{1}{K} \) (Reciprocal of bulk modulus)
Relation between Moduli
The relationship among these moduli is given by the following equations:
- \( E = 2G(1 + \nu) \) (where \( \nu \) is Poisson's ratio)
- \( K = \frac{E}{3(1 - 2\nu)} \)
These relationships can also be expressed in terms of their reciprocals.
Deriving the Relationships
To derive the correlation between x, y, and z, we can use the known relationships:
1. From \( E = 2G(1 + \nu) \), we express \( G \) in terms of \( E \) and \( \nu \):
- \( G = \frac{E}{2(1 + \nu)} \)
2. From \( K = \frac{E}{3(1 - 2\nu)} \), we can express \( E \) in terms of \( K \) and \( \nu \):
- \( E = 3K(1 - 2\nu) \)
By substituting these values and manipulating the equations, you can derive a relationship that links x, y, and z.
Final Result and Conclusion
The correct correlation derived from the relationships is:
- \( x = \frac{3y + z}{9} \)
Thus, option 'A' is indeed the correct answer. This relationship highlights the interplay between the different types of elastic moduli and their influence on material behavior.
The question revolves around the relationships between three fundamental material properties: Young's modulus of elasticity (E), modulus of rigidity (G), and bulk modulus of elasticity (K). Their reciprocals are defined as:
- \( x = \frac{1}{E} \) (Reciprocal of Young's modulus)
- \( y = \frac{1}{G} \) (Reciprocal of modulus of rigidity)
- \( z = \frac{1}{K} \) (Reciprocal of bulk modulus)
Relation between Moduli
The relationship among these moduli is given by the following equations:
- \( E = 2G(1 + \nu) \) (where \( \nu \) is Poisson's ratio)
- \( K = \frac{E}{3(1 - 2\nu)} \)
These relationships can also be expressed in terms of their reciprocals.
Deriving the Relationships
To derive the correlation between x, y, and z, we can use the known relationships:
1. From \( E = 2G(1 + \nu) \), we express \( G \) in terms of \( E \) and \( \nu \):
- \( G = \frac{E}{2(1 + \nu)} \)
2. From \( K = \frac{E}{3(1 - 2\nu)} \), we can express \( E \) in terms of \( K \) and \( \nu \):
- \( E = 3K(1 - 2\nu) \)
By substituting these values and manipulating the equations, you can derive a relationship that links x, y, and z.
Final Result and Conclusion
The correct correlation derived from the relationships is:
- \( x = \frac{3y + z}{9} \)
Thus, option 'A' is indeed the correct answer. This relationship highlights the interplay between the different types of elastic moduli and their influence on material behavior.
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If x, y and z are the reciprocal of the Youngs modulus of elasticity, modulus of rigidity and bulk modulus of elasticity respectively, the correct correlation is,a)x = (3y + z)/9b)x = (9y +z)/9c)x = (y + 3z)/9d)x = (3y + 2z)/9Correct answer is option 'A'. Can you explain this answer?
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