The elastic potential energy stored per unit volume of a stretched wire is equal to
- A.Stress multiplied by strain
- B.One half multiplied by stress multiplied by strain
- C.Stress divided by strain
- D.Two multiplied by stress multiplied by strain
Correct answer
Explanation
The correct answer is B, one half multiplied by stress multiplied by strain. The restoring force grows from zero to its final value as the wire is stretched, so the work done is the average force multiplied by the extension, and dividing by the volume of the wire leaves half the product of stress and strain as the energy stored in each unit of volume. It is the same half that appears in the expression for the energy of a stretched spring. Option A is wrong because it omits that factor of one half and would be true only if the full force acted through the whole extension. Option C is wrong because stress divided by strain is the modulus of elasticity, which has the unit of stress and not of energy density. Option D is wrong because it doubles the correct value with no physical basis. The result can also be written as half the modulus multiplied by the square of the strain.
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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