A composite bar is made of steel and aluminium strips each having 3 square centimetre area of cross-section. The composite bar is subjected to an axial load of 12000 newton. If the Young's modulus of steel is three times that of aluminium, the stress in steel is
- A.10 newton per square millimetre
- B.20 newton per square millimetre
- C.30 newton per square millimetre
- D.None of the above
Correct answer
Explanation
The correct answer is C, 30 newton per square millimetre. The two strips are joined and carry the load together, so they suffer the same strain. Since stress equals the modulus multiplied by the strain, the stress in steel is three times the stress in aluminium. Each strip has an area of 3 square centimetres, which is 300 square millimetres, so the total load is 300 multiplied by the sum of the two stresses, that is 300 multiplied by four thirds of the steel stress, giving 400 times the steel stress. Setting that equal to 12000 newton gives a steel stress of 30 newton per square millimetre. Option A is wrong because 10 is the stress in the aluminium strip, one third of the answer. Option B is wrong because 20 would follow only if the load were shared equally, ignoring the difference in modulus. Option D is wrong because a correct value is present among the choices.
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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