Physics · Mechanical Properties Of Solids · NEET
It is stress divided by strain: Y = tensile stress / longitudinal strain. Strain has no unit, so Y takes the unit of stress (N/m² or pascal). If you flip it and write strain/stress, you get compliance, not Young's modulus. Rule for NEET: modulus is always stress on top.
Because it measures how strongly a material resists a change in length and springs back. A large Young's modulus means the material resists stretching and returns to its original length, which is what 'elastic' means. It is the elastic modulus for pulling or pushing along a length (tensile or compressive), not for twisting or squeezing from all sides.
No. Young's modulus is a property of the material only, not of the shape. Steel has the same Y whether the wire is thin or thick, long or short. What changes with shape is the elongation ΔL = FL/(AY): a longer wire stretches more, a thicker wire stretches less, but Y itself stays fixed for that material.
Young's modulus Y depends only on the material. Stiffness (the force per unit stretch, k = AY/L) also depends on the wire's length and area. Two steel wires have the same Y but different stiffness if their length or thickness differ. NEET often tests this: same material, different size, different force needed.
From ΔL = FL/(AY): elongation is directly proportional to length L and inversely proportional to area A. A shorter wire (small L) has less material to stretch, and a thicker wire (large A) spreads the force over more atoms, so each layer stretches less. Y stays the same because it is a material constant.
Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δl on applying a force F, how much force is needed to stretch the second wire by the same amount?
The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus respectively are 8 × 10⁸ N m⁻² and 2 × 10¹¹ N m⁻², is
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.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Y = tensile stress / longitudinal strain = (F/A) / (ΔL/L) = FL / (A·ΔL), where F is the applied force, A is the cross-sectional area, L is the original length, and ΔL is the increase in length.
The SI unit is newton per square metre (N/m²), also called the pascal (Pa). Because strain has no unit, Young's modulus carries the same unit as stress. Its dimensional formula is [ML⁻¹T⁻²].
It is a scalar. It is the ratio of two magnitudes (stress and strain), so it has size but no direction.
Steel. Steel has a Young's modulus of about 2 × 10¹¹ N/m², while rubber is far lower. A higher Young's modulus means the material is stiffer and stretches less for the same stress, so steel is much stiffer than rubber.
It is the most tested elastic constant in Mechanical Properties of Solids. Nearly every NEET numerical on stretching a wire uses ΔL = FL/(AY), elastic potential energy, or comparing materials, so knowing the definition and formula well is essential.
