Physics · Mechanical Properties Of Solids · NEET
Not exactly. 'Modulus of elasticity' is the general name for the ratio stress/strain. There are three specific types: Young's modulus (Y, for length change), shear modulus (G or η, for shape change) and bulk modulus (B, for volume change). Young's modulus is only ONE of the three. So every Young's modulus is a modulus of elasticity, but not every modulus of elasticity is Young's modulus.
Modulus = stress / strain. Strain is a pure ratio (length/length or volume/volume), so it has no unit. Dividing by a number-with-no-unit does not remove the unit of stress. So the modulus keeps exactly the same unit as stress: N/m² or pascal (Pa). This is a very common NEET trap.
SI unit = N/m² = pascal (Pa), same as stress and pressure. Dimensional formula = [ML⁻¹T⁻²]. You get this from stress = force/area = (MLT⁻²)/(L²) = ML⁻¹T⁻², and strain is dimensionless, so the modulus has the same dimensions as stress.
Less. E = stress/strain, so for the same stress a larger modulus gives a smaller strain. A high modulus means the material is stiffer (harder to deform). Steel has a much larger Young's modulus than rubber, so steel stretches far less for the same pulling stress — that is why steel is called 'more elastic'.
It is a property of the MATERIAL, not the shape or size. Two wires of the same metal but different length or thickness have the same Young's modulus. The actual elongation depends on length and area, but the modulus (stress/strain) stays constant for that material at a given temperature.
Match List I with List II. List I: A. Young's Modulus, B. Compressibility, C. Bulk Modulus, D. Poisson's Ratio. List II: I. (Δd/d)/(ΔL/L), II. FL/(A·ΔL), III. -(1/V)(ΔV/P), IV. -V·P/ΔV. Choose the correct answer.
Dimensions of stress are:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Modulus of elasticity E = stress / strain, valid within the elastic limit (Hooke's law region). For length change it is Young's modulus, for shape change it is shear modulus, and for volume change it is bulk modulus.
The SI unit is N/m², also called the pascal (Pa). It is the same as the unit of stress and pressure because strain is dimensionless.
The dimensional formula is [ML⁻¹T⁻²], identical to stress and pressure.
Three: Young's modulus (Y), shear modulus or modulus of rigidity (G), and bulk modulus (B). Each is a stress divided by its corresponding strain.
Steel needs much more stress to produce the same strain, so its stress/strain ratio (modulus) is far larger. A larger modulus means greater stiffness and greater elasticity, which is why steel resists deformation more than rubber.
