Consider the following statements regarding mechanical properties of solids: 1. The ratio of tensile stress to longitudinal strain is defined as bulk modulus. 2. The ratio of hydraulic stress to corresponding hydraulic strain is called Young's modulus. 3. The ratio of shearing stress to corresponding shearing strain is called modulus of rigidity. Which of the statements given above is/are correct?

Correct — C, 3 only. Only the third statement is right: the ratio of shearing stress to shearing strain is indeed the modulus of rigidity, also called the shear modulus. Statement 1 misnames Young's modulus — the ratio of tensile stress to longitudinal strain — as bulk modulus. Statement 2 misnames the bulk modulus — the ratio of hydraulic or volumetric stress to the corresponding volumetric strain — as Young's modulus. The examiner has simply exchanged the two labels, leaving the third definition untouched, so exactly one statement survives.

• (a)1 and 2 only — Accepts precisely the two statements whose names have been swapped and rejects the one that is correct. It is the exact inverse of the right answer.
• (b)2 and 3 only — Keeps the correct third statement but also accepts the second, which calls the bulk modulus by Young's name. Hydraulic stress produces a change in volume, and the modulus for that is the bulk modulus.
• (d)1, 2 and 3 — Would require all three names to be right, but two have been exchanged. A quick check on the physical situation each describes — stretching a wire, squeezing a body from all sides, sliding one face over another — separates them immediately.

Within the elastic limit, stress is proportional to strain, and the constant of proportionality is a modulus of elasticity. Three moduli cover the three ways a body can be deformed. Young's modulus applies to a lengthwise pull or push: tensile or longitudinal stress over longitudinal strain. The bulk modulus applies to uniform pressure from all sides: hydraulic stress over the fractional change in volume; its reciprocal is compressibility. The modulus of rigidity applies to a tangential force sliding one face relative to another: shearing stress over shearing strain. Solids possess all three; a fluid at rest has only a bulk modulus, since it cannot sustain a shear.

This item is a pure label-swap, and the reliable defence is to attach each modulus to a physical picture rather than to a formula. Stretching a wire is Young. Taking a metal ball to the bottom of the sea is bulk. Pushing the top cover of a thick book sideways while the bottom stays put is rigidity. Once the pictures are in place, statements 1 and 2 read as obviously mismatched, and the item collapses to a single surviving statement.

• Young's modulus is the ratio of tensile (longitudinal) stress to longitudinal strain.
• The bulk modulus is the ratio of hydraulic (volumetric) stress to volumetric strain.
• The modulus of rigidity, or shear modulus, is the ratio of shearing stress to shearing strain.
• The reciprocal of the bulk modulus is compressibility.
• Fluids at rest have a bulk modulus but no modulus of rigidity, because they cannot resist a shearing stress.

• Reading a statement for its shape and marking it correct because the words stress and strain both appear.
• Confusing hydraulic stress with tensile stress; one changes volume, the other changes length.
• Assuming all three moduli exist for every material; a fluid at rest has no shear modulus.

A definition item built by swapping two labels, so it rewards attaching each modulus to a picture rather than to a phrase.

No directly related past PYQ was found.

• practice — not a real PYQ

  The reciprocal of the bulk modulus of a material is called its

  • (a)rigidity
  • (b)compressibility
  • (c)Poisson's ratio
  • (d)elastic limit

  Answer(b) compressibility — a highly compressible substance has a small bulk modulus.

• practice — not a real PYQ

  A liquid at rest has no modulus of rigidity because it

  • (a)has no volume
  • (b)cannot sustain a shearing stress
  • (c)is incompressible
  • (d)has no free surface

  Answer(b) cannot sustain a shearing stress — a liquid flows under a tangential force instead of resisting it elastically.