JEE · Physics
Explain how a solid resists deformation using stress, strain and the elastic moduli, choose the correct modulus and formula condition for a given loading, and diagnose common stress-strain mistakes.
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In short
Elasticity describes how a solid deforms under load and returns to its original shape when the load is removed, provided the deformation stays within the elastic limit. Stress is the internal restoring force per unit area, strain is the fractional deformation, and the elastic modulus is the ratio of stress to strain for a given type of deformation.
A correct solution first identifies the type of deformation (length, volume or shape), then picks the matching modulus (Young's, bulk or shear) and checks that the load stays within the region where Hooke's law holds.
The official JEE documents define content scope. They do not publish chapter weightage, so none is asserted here.
Verified against the current JEE Main 2026 syllabus (Unit 7, Properties of Solids and Liquids) and JEE Advanced 2026 syllabus on 8 September 2026. This is a wording and scope mapping, not a claim about question difficulty or frequency.
Sources: JEE Main 2026 syllabus and JEE (Advanced) 2026 syllabus, both linked in the sources section below.
Prerequisite
Units and Measurements
Stabilise SI units, dimensions and significant figures before working with moduli.
Prerequisite
Laws of Motion
Force, equilibrium and free-body reasoning are used to define internal stress.
Parent
JEE Physics
Subject hub for the Physics chapter set.
Parent
JEE syllabus
Exam-level official scope for every Physics, Chemistry and Mathematics unit.
This is a readiness check, not a weightage or scoring-priority list.
Stress is force divided by the area over which it acts internally, not the external applied force by itself.
When an external force deforms a solid, internal forces resist the deformation. Stress is this internal restoring force divided by the cross-sectional area over which it acts. Its SI unit is the same as pressure, newton per square metre.
Strain compares the change caused by deformation to the original undeformed value.
Longitudinal strain is change in length divided by original length. Volume strain is change in volume divided by original volume. Shear strain is the angle of deformation, measured in radians. All three are ratios of like quantities, so strain has no unit.
Stress is proportional to strain only up to the proportional limit on the stress-strain curve.
Hooke's law states that stress is proportional to strain for small deformations. Beyond the proportional limit the material can still be elastic for a short range, but the linear relationship no longer holds, and beyond the elastic limit the deformation becomes permanent.
Young's modulus is for length change under longitudinal stress, bulk modulus is for volume change under uniform pressure, shear modulus is for shape change under tangential stress.
Young's modulus applies to a rod or wire stretched or compressed along its length. Bulk modulus applies to a body under uniform pressure from all sides, such as a fluid or a submerged solid. Shear modulus (modulus of rigidity) applies when tangential stress changes shape without changing volume.
Proportional region, elastic limit, yield point, plastic region, and fracture point occur in order.
A tensile test produces a stress-strain curve with a straight proportional region, followed by a region where the material remains elastic but the relation is no longer linear, a yield point where plastic deformation begins, a plastic region, and finally fracture. Only the region up to the elastic limit is described by Hooke's law.
Poisson's ratio is the negative ratio of lateral strain to longitudinal strain, within elastic limits.
When a wire is stretched, it also contracts sideways. Poisson's ratio compares this lateral contraction strain to the longitudinal extension strain. It is a material property used alongside the elastic moduli in NCERT-level treatment of elasticity, and it is not named as a separate line item in the current official JEE Main or JEE Advanced syllabus documents.
Compressibility measures how readily a substance's volume changes under pressure and is defined as the reciprocal of the bulk modulus. It is a standard supporting idea for bulk modulus problems rather than a separately notified syllabus topic.
Energy stored in a stretched wire equals the work done against the internal restoring force.
As a wire is stretched gradually within the elastic limit, work is done against the internal restoring force, and this work is stored as elastic potential energy. It can be recovered as the wire returns to its natural length, provided the elastic limit was not exceeded.
If a rod that would otherwise expand or contract with a temperature change is rigidly constrained at both ends, an internal thermal stress develops instead of a length change. This connects thermal expansion to Young's modulus and is treated as an application of the same stress-strain framework.
Match the type of deformation to the correct modulus before any algebra.
Stress equals force divided by area.
Internal restoring force per unit cross-sectional area.
Use when — A deforming force acts on a defined cross-sectional area within the elastic limit.
Common trap — Using the externally applied force without confirming it equals the internal restoring force in equilibrium.
Longitudinal strain equals change in length divided by original length.
Fractional change in length of a stretched or compressed rod or wire.
Use when — The deformation is along one dimension, such as a stretched wire.
Common trap — Using the final length instead of the original length in the denominator.
Volume strain equals change in volume divided by original volume.
Fractional change in volume under uniform pressure.
Use when — A body is under uniform pressure from all sides.
Common trap — Applying volume strain to a deformation that only changes shape, not volume.
Shear strain equals the tangent of the shear angle, approximately the angle itself for small angles.
Angular deformation produced by a tangential force, for small angles.
Use when — A tangential stress changes the shape of a block without changing its volume, and the angle is small.
Common trap — Treating shear strain as a length ratio instead of an angle.
Stress equals a constant times strain, within the proportional limit.
Stress is directly proportional to strain within the proportional limit.
Use when — The deformation is within the proportional (linear) part of the elastic region.
Common trap — Extending the linear relation beyond the elastic limit shown on the stress-strain curve.
Young's modulus equals longitudinal stress divided by longitudinal strain.
Ratio of longitudinal stress to longitudinal strain for a stretched or compressed rod or wire.
Use when — The deformation is along the length of a rod or wire, within the elastic limit.
Common trap — Using Young's modulus for a volume or shape change instead of Young's, bulk or shear as appropriate.
Bulk modulus equals negative pressure change divided by fractional volume change.
Ratio of pressure change to fractional volume change, for uniform compression or expansion.
Use when — A body is under uniform pressure from all sides and only its volume changes.
Common trap — Dropping the negative sign convention that reflects volume decreasing as pressure increases.
Shear modulus equals shear stress divided by shear strain.
Ratio of tangential (shear) stress to shear strain.
Use when — A tangential force deforms the shape of a body without changing its volume, within the elastic limit.
Common trap — Confusing shear modulus with Young's modulus when the loading is tangential, not longitudinal.
Compressibility equals one divided by bulk modulus.
Compressibility is the reciprocal of bulk modulus.
Use when — Bulk modulus is known and the ease of volume change under pressure is asked for.
Common trap — Reporting compressibility with the same numerical value as bulk modulus instead of inverting it.
Poisson's ratio equals negative lateral strain divided by longitudinal strain.
Ratio comparing sideways contraction strain to lengthwise extension strain.
Use when — Both lateral and longitudinal strains are given or asked for, within the elastic limit.
Common trap — Dropping the sign convention that keeps Poisson's ratio positive for materials that contract sideways while stretched.
Elastic potential energy equals one half times force times extension, for gradual loading.
Elastic potential energy stored in a wire stretched gradually within the elastic limit.
Use when — A wire or rod is stretched gradually (not suddenly) and stays within the elastic limit.
Common trap — Using the final force F over the full extension instead of the average force during gradual loading.
Elastic energy per unit volume equals one half times stress times strain.
Elastic potential energy stored per unit volume of a stretched wire.
Use when — Volume of the stretched material is known and energy density is required instead of total energy.
Common trap — Mixing stress and strain from different loading stages instead of the final elastic-limit values.
Thermal stress equals Young's modulus times the coefficient of linear expansion times the temperature change.
Internal stress developed in a rigidly constrained rod when its free thermal expansion is prevented.
Use when — Both ends of a rod are rigidly fixed so the rod cannot expand or contract with a temperature change.
Common trap — Applying this formula when the rod is free to expand, where no thermal stress develops.
Answer: F = Y × A × (ΔL/L), evaluated with the given numerical values.
Compute longitudinal strain: ΔL / L = 0.001 m / 2 m.
Use Y = (F/A) / (ΔL/L) rearranged to F = Y × A × (ΔL/L), substituting the known Young's modulus, area and strain.
Confirm the resulting stress is below the elastic limit of steel before accepting the answer.
Answer: B = -ΔP / (ΔV/V); compressibility k = 1/B.
Identify the loading as uniform pressure from all sides, so bulk modulus is the correct choice, not Young's or shear modulus.
Apply B = -ΔP / (ΔV/V) using the given pressure increase and fractional volume decrease.
Take the reciprocal of B to state the compressibility.
Answer: Thermal stress = Y × alpha × ΔT.
Recognise that the rod would expand by alpha × L × ΔT if free, so the constraint imposes an equivalent compressive strain of alpha × ΔT.
Apply stress = Y × strain with this thermally imposed strain to get stress = Y × alpha × ΔT.
Applying Hooke's law (stress proportional to strain) beyond the elastic limit shown on the stress-strain curve.
Knowledge gapWhy it happens
The linear relation only holds up to the proportional limit; beyond the elastic limit deformation becomes permanent and non-linear.
How it is corrected
Check where the given deformation lies on the stress-strain curve before using a linear stress-strain formula.
Using Young's modulus for a problem that describes uniform pressure (volume change) or tangential force (shape change).
Decision / selection errorWhy it happens
Each modulus is defined for a specific type of deformation; they are not interchangeable.
How it is corrected
Identify whether length, volume or shape is changing before selecting Young's, bulk or shear modulus.
Treating stress as the applied external force rather than the internal restoring force per unit area.
Recall gapWhy it happens
In equilibrium the two are numerically equal, but the physical meaning of stress is internal and distributed over area, not a single external force.
How it is corrected
Always divide by the correct cross-sectional area and confirm equilibrium before equating applied force to internal stress.
Dropping the negative sign in the bulk modulus formula and reporting a negative modulus.
Execution errorWhy it happens
Volume decreases as pressure increases, so the negative sign keeps bulk modulus a positive quantity.
How it is corrected
Track the sign of ΔV relative to ΔP explicitly before finalising the numerical answer.
Using the gradual-loading energy formula (1/2) F ΔL when a load is applied suddenly.
Decision / selection errorWhy it happens
Sudden loading involves a different work-energy relationship because the force is not built up gradually.
How it is corrected
Check whether the problem states gradual or sudden loading before applying the (1/2) F ΔL energy formula.
Computing shear strain as a length ratio instead of an angle.
Knowledge gapWhy it happens
Shear strain is defined through the angular deformation of the body, not a change-in-length ratio.
How it is corrected
Identify the shear angle from the geometry of the deformed shape before computing shear modulus.
Calculating thermal stress for a rod that is free to expand, where no stress develops.
Decision / selection errorWhy it happens
Thermal stress requires a constraint that prevents the natural length change; a free rod simply changes length instead.
How it is corrected
Confirm the rod is rigidly constrained at both ends before applying the thermal stress formula.
Mixing units for force, area and length when computing a modulus, producing an inconsistent numerical answer.
Execution errorWhy it happens
Moduli combine force, area and a dimensionless strain; any unit inconsistency propagates directly into the result.
How it is corrected
Convert all quantities to consistent SI units before substituting into a modulus formula.
Assuming Poisson's ratio, compressibility, or thermal stress are heavily tested because they appear in coaching notes.
Needs reviewWhy it happens
These are standard supporting concepts in NCERT-level treatment, but they are not named as separate line items in the current official JEE Main or JEE Advanced syllabus documents.
How it is corrected
Check the official syllabus mapping table on this page and the linked source documents before assuming exam-specific emphasis.
FAQ
Straight answers about how Rank Sarthi fits into serious exam preparation.
No. This chapter covers how solids deform under stress and strain. Fluid Mechanics and Surface Tension are separate chapters that own pressure-in-fluids and surface-force intents respectively.
They are not named as separate line items in the current official JEE Main or JEE Advanced syllabus documents. They are treated here as standard NCERT-level supporting concepts for bulk modulus and strain analysis. Check the official documents directly for confirmation.
Young's modulus applies to length change under longitudinal stress, bulk modulus applies to volume change under uniform pressure, and shear modulus applies to shape change under tangential stress.
Hooke's law holds only up to the proportional limit on the stress-strain curve. Beyond that, the material may still be elastic for a short range, but the linear relation between stress and strain no longer holds.
Thermal expansion is a length or volume change when a material is free to respond to temperature change. Thermal stress develops instead when that expansion or contraction is rigidly prevented.
No. Weightage, trend percentages and question-count forecasts are deliberately not published on this page.
SI units and dimensions, and force and equilibrium reasoning from Laws of Motion, since stress is defined through internal restoring force.
Evidence boundary: the syllabus mapping is tied to the official 2026 JEE Main and JEE Advanced documents. Poisson's ratio, compressibility, elastic potential energy and thermal stress are standard NCERT-level supporting concepts, not independently notified syllabus line items, and this page states that boundary explicitly. No chapter weightage, question frequency or forecast is asserted.
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