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For a given material, the Young's modulus is 2. 4 times that of rigidity modulus. Its Poisson's ratio is
- a)2.4
- b)1.2
- c)0.4
- d)0.2
Correct answer is option 'D'. Can you explain this answer?
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For a given material, the Young's modulus is 2. 4 times that of rigid...
Young's modulus (E) is a measure of a material's stiffness or resistance to deformation under tensile or compressive stress. It is defined as the ratio of stress to strain in the elastic region of the material. Mathematically, Young's modulus can be expressed as:
E = (stress)/(strain)
Rigidity modulus (G), also known as shear modulus or modulus of rigidity, is a measure of a material's resistance to shear deformation. It is defined as the ratio of shear stress to shear strain. Mathematically, rigidity modulus can be expressed as:
G = (shear stress)/(shear strain)
Poisson's ratio (ν) is a measure of the ratio of lateral strain to longitudinal strain when a material is under longitudinal stress. It is defined as the negative ratio of transverse strain to longitudinal strain. Mathematically, Poisson's ratio can be expressed as:
ν = -(lateral strain)/(longitudinal strain)
Given that Young's modulus (E) is 2.4 times that of rigidity modulus (G), we can write:
E = 2.4G
To find Poisson's ratio (ν), we can use the relationship between Young's modulus, rigidity modulus, and Poisson's ratio:
ν = (E - 2G)/(2(E - G))
Substituting the value of E = 2.4G, we have:
ν = (2.4G - 2G)/(2(2.4G - G))
= (0.4G)/(2G)
= 0.4/2
= 0.2
Therefore, the correct answer is option 'D' - Poisson's ratio is 0.2.
E = (stress)/(strain)
Rigidity modulus (G), also known as shear modulus or modulus of rigidity, is a measure of a material's resistance to shear deformation. It is defined as the ratio of shear stress to shear strain. Mathematically, rigidity modulus can be expressed as:
G = (shear stress)/(shear strain)
Poisson's ratio (ν) is a measure of the ratio of lateral strain to longitudinal strain when a material is under longitudinal stress. It is defined as the negative ratio of transverse strain to longitudinal strain. Mathematically, Poisson's ratio can be expressed as:
ν = -(lateral strain)/(longitudinal strain)
Given that Young's modulus (E) is 2.4 times that of rigidity modulus (G), we can write:
E = 2.4G
To find Poisson's ratio (ν), we can use the relationship between Young's modulus, rigidity modulus, and Poisson's ratio:
ν = (E - 2G)/(2(E - G))
Substituting the value of E = 2.4G, we have:
ν = (2.4G - 2G)/(2(2.4G - G))
= (0.4G)/(2G)
= 0.4/2
= 0.2
Therefore, the correct answer is option 'D' - Poisson's ratio is 0.2.
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For a given material, the Young's modulus is 2. 4 times that of rigidity modulus. Its Poisson's ratio isa)2.4b)1.2c)0.4d)0.2Correct answer is option 'D'. Can you explain this answer?
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For a given material, the Young's modulus is 2. 4 times that of rigidity modulus. Its Poisson's ratio isa)2.4b)1.2c)0.4d)0.2Correct answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about For a given material, the Young's modulus is 2. 4 times that of rigidity modulus. Its Poisson's ratio isa)2.4b)1.2c)0.4d)0.2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a given material, the Young's modulus is 2. 4 times that of rigidity modulus. Its Poisson's ratio isa)2.4b)1.2c)0.4d)0.2Correct answer is option 'D'. Can you explain this answer?.
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