Poisson's ratio of a material is defined as the ratio of
- A.Stress to strain
- B.Lateral strain to longitudinal strain
- C.Longitudinal strain to lateral strain
- D.Shear stress to shear strain
Correct answer
Explanation
The correct answer is B, lateral strain to longitudinal strain. When a wire is pulled it lengthens and at the same time grows thinner, and Poisson's ratio records how large the sideways contraction is compared with the lengthwise extension; it is a pure number, with theoretical limits of minus one and one half and practical values of about 0.2 to 0.4. Option A is wrong because the ratio of stress to strain is a modulus of elasticity, measured in pascal, not a dimensionless ratio. Option C is wrong because it inverts the definition, and the inverted quantity is not given any name in the syllabus. Option D is wrong because shear stress divided by shear strain is the modulus of rigidity. A material with a Poisson's ratio near one half, such as rubber, keeps its volume almost unchanged when it is stretched.
Read the full article: Elasticity, Stress, Strain and Hooke's Law: Exam Notes
Practice Questions
View allHooke's law states that within the elastic limit
- A.Stress is directly proportional to strain
- B.Stress is inversely proportional to strain
- C.Strain is independent of stress
- D.Stress is proportional to the square of the strain
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Hooke found that so long as a body is not strained beyond its elastic limit, the restoring force per unit area rises in step with the fractional deformation, and the constant ratio of the two is called the modulus of elasticity.
Read the full explanation →The SI unit of stress is the
- A.Newton
- B.Joule
- C.Pascal
- D.Watt
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Stress is the restoring force divided by the area over which it acts, so its unit is the newton per square metre, and that combination is given the special name pascal, the same unit used for pressure.
Read the full explanation →Strain is a quantity that has
- A.The unit newton per square metre
- B.No unit and no dimensions
- C.The unit metre
- D.The same unit as energy
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Strain is defined as the change in a dimension divided by the original value of the same dimension, a length divided by a length or a volume divided by a volume, so the units cancel and only a pure number survives.
Read the full explanation →The ratio of longitudinal stress to longitudinal strain within the elastic limit is called
- A.Bulk modulus
- B.Modulus of rigidity
- C.Young's modulus
- D.Poisson's ratio
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It governs the stretching or compression of a wire or rod along its length and is obtained by dividing the force per unit area of cross section by the fractional change in length.
Read the full explanation →The reciprocal of the bulk modulus of a material is known as its
- A.Compressibility
- B.Rigidity
- C.Ductility
- D.Tenacity
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The bulk modulus measures how strongly a substance resists a change in volume under uniform pressure, so its reciprocal measures how readily the volume yields, and that quantity is called compressibility.
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