Physics · Mechanical Properties Of Solids · NEET
Both are Hooke's law, but NEET (Class 11 NCERT) states it as: stress is directly proportional to strain, so stress = k x strain. The spring version (F = kx, force proportional to extension) is a special case of the same idea. In the NCERT statement, k is the modulus of elasticity. In the spring version, k is the spring constant. Read the question: if it gives stress and strain, use stress = k x strain; if it gives force and extension of a spring, use F = kx.
k is the proportionality constant called the modulus of elasticity. It equals stress divided by strain (k = stress/strain) and is a fixed property of the material, not of the sample size. Its SI unit is the same as stress, N/m^2 (pascal), because strain has no units. Different types of deformation give different moduli: Young's modulus (Y) for length change, shear modulus (G) for shape change, and bulk modulus (B) for volume change.
Hooke's law is valid only up to the proportional limit (point A on the stress-strain curve), where the graph is a straight line. Beyond A, the body may still be elastic (returns to shape) up to the elastic limit / yield point B, but stress and strain are NO LONGER proportional there. So: elastic behaviour lasts longer than Hooke's law. A body can obey elasticity but disobey Hooke's law in the region between proportional limit and elastic limit.
No, not over most of its range. NCERT points out that elastic materials like rubber and the elastic tissue of the aorta can be stretched a lot and still return to shape (they are elastic), but their stress-strain graph is a curve, not a straight line. Since stress is not proportional to strain, they do NOT obey Hooke's law over most of the region. Hooke's law is only for small deformations of ordinary solids like metals.
NCERT calls Hooke's law an empirical law, meaning it is based on experiment and observation, not derived from a deeper theory. It works well for many materials for small strains but it is an approximation - it fails for large deformations and for materials like rubber. This is a common one-word NTA fill-in-the-blank: Hooke's law is empirical and holds only for small deformations.
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 x 10^8 N/m^2 and 2 x 10^11 N/m^2, is
Try the real previous-year questions from this chapter — each with the answer and a full solution.
For small deformations, the stress in a body is directly proportional to the strain produced in it. In symbols: stress is proportional to strain, so stress = k x strain, where k is the modulus of elasticity of the material.
The unit of k (modulus of elasticity) is N/m^2, also called the pascal (Pa). This is because k = stress/strain, stress has units N/m^2, and strain is a pure number with no units.
It is an empirical law. It is based on experimental observation and works only as an approximation for small strains; it is not derived from any deeper principle and fails for large deformations.
Hooke's law fails for large deformations, so it holds only for small strains up to the proportional limit. It does not apply to elastomers like rubber whose stress-strain graph is curved, and beyond the proportional limit stress and strain are no longer proportional.
Only if the applied stress stays within the proportional limit. NEET problems using Y = stress/strain assume Hooke's law holds. If the stress equals the elastic limit, you get the maximum elongation while still elastic, as in the 2024 PYQ.
