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CBSE Class 11 · Physics

Mechanical Properties of Solids

Official NCERT chapter from Physics Part I–II (book code keph1). ExamMaster notes are original teaching at CBSE Class 11 depth.

This lesson follows the official chapter “Mechanical Properties of Solids” in Physics Part I–II. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 11
  • Medium level
  • 8 concepts

1Stress and strain

Stress is force over area; strain is change-in-size over original size. 80 N on 2×10⁻⁴ m² is 4×10⁵ N/m². Strain has no unit. A fat force on a fat area can be a small stress. Stress is not the force alone.

Calling 80 N the stress is the heading-steal.

Figure. Equal 80 N pulls, same drawn length, act on a 2 mm² bar of length 2.5 m. Stress is force over the area that carries it; strain is the stretch over the original length. The millimetre-scale extension is written in later concepts, not drawn — at this scale it would be 0.02% of L and invisible.

How it works

  1. Name F and A, or ΔL and LThe given.
  2. Write F/A and ΔL/LStress and strain.
  3. Keep N/m² and a pure numberThe pair.

2Hooke’s law

Hooke’s law (school elastic): stress ∝ strain, so F ∝ ΔL, or stress = Y × strain with Y the taught modulus, in the linear range. A 2 mm stretch under 40 N that doubles when F doubles is this law. Past the linear bit, Hooke no longer owns the curve.

Using Hooke after the lesson’s break-point is a miss.

Figure. Hooke’s law is the straight line through the origin: F grows in step with ΔL, here 80 N at 0.50 mm so k = 1.6 × 10^5 N/m. The three plotted points sit on y = x in the axis frame. Past the elastic limit this line is not the material.

How it works

  1. Stay in the linear rangeThe gate.
  2. Write F = k ΔL or stress = Y strainThe law.
  3. Refuse a plastic leftover as this headingElastic only.

40 N → 2 mm, Hooke

If Hooke holds, what stretch at 80 N?

  • Double Fdouble ΔL
  • Stretch4 mm
  • ReadLinear range assumed

Pro tip. F ∝ ΔL only while the law holds.

3Stress-strain curve

A stress–strain curve is a graph: linear start (Hooke), then a taught yield/break if named. The slope in the linear bit is the modulus-story. A curve is a look, not a second law. One material’s sketch is enough.

Reading the last point as Y is a miss if that point is past linear.

Figure. OP is the only Hooke stretch: its slope in the axis frame is Y. E is the last return-to-zero point, Y the yield, U the highest stress, F the break. The strain axis is stretched through the elastic part — a real metal yields at ε ~ 0.001, which would be a hair on a true-scale axis.

How it works

  1. Mark the linear bitThe Hooke-region.
  2. Read slope as the modulus-storyThe curve’s job.
  3. Name yield only if the lesson marked itHonest.

4Elastic moduli

Elastic moduli: Young’s Y = (F/A)/(ΔL/L), shear, bulk — as taught. A large Y means a small strain for a given stress (stiff). Y is not k of a particular spring unless you convert with geometry.

Using Y as a force is a unit-miss.

Figure. Three moduli, three loads. Y is axial pull on a rod. B is the same pressure inward on every face of a block. η is a couple that slides one face: the dashed rectangle is the unsheared shape, the solid parallelogram is the sheared one. Not to a common force scale.

How it works

  1. Name which modulus (stretch, shear, volume)The kind.
  2. Write stress/strain for that kindThe modulus.
  3. Keep N/m²A stiffness of the material.

5Applications of elastic behaviour of materials

Applications: a beam that sags, a cable that stretches, a taught safety-margin — the heading is “use the modulus to size ΔL”, not a construction-site tour. One cable 2 m long, A and Y given, is enough.

A skyline-photo is a setting.

Figure. A floor beam is stiffer when steel sits far from the mid-plane. The I-section puts flanges at the top and bottom; a solid plank of the same height leaves metal near the middle where it adds little bending resistance. Schematic sections — not a mill-drawing.

How it works

  1. Name F, A, L, YThe given.
  2. Compute ΔL = (F L)/(A Y)The use.
  3. Keep it one honest stretchThis class.

6A definition is a test you can run

Stress / Hooke is a test: F/A, ΔL/L, or the linear link. If you only say “elastic”, you have a heading.

A rubber-band advert is not the test.

Figure. Stress is not a look. ‘It looks stiff’ is not a measurement. The definition is the ratio you can run: name F, name the area that carries it, divide. Same bar as the first concept — 80 N on 2 mm² is 40 MPa.

How it works

  1. Name F, A, ΔL, LThe object.
  2. Give stress, strain, or YThe test.
  3. Then the word has contentThe definition ran.

7Name the given before the unknown

The given are F, A, L. The unknown is ΔL or Y. Copy mm versus m before you divide.

Using A=2 because the write was 2×10⁻⁴ is a silent drop of 10⁻⁴.

Figure. Write the given first: F = 80 N, L = 2.5 m, A = 2 mm². The unknown is the stretch. Do not reach for Y until those three are named. The extension is the ask, not a fourth given.

How it works

  1. Copy F, A, L in SIThe given.
  2. Name stress or ΔLThe unknown.
  3. Then divideGiven first.

8One worked case is enough at this class

One linear stretch is enough. A page of the same 4 mm clone does not add a new bulk modulus.

Ten twins of 40 N are still one idea.

Figure. One Class 11 case. Y = FL/(AΔL) = 80 × 2.5 / (2.0×10⁻⁶ × 5.0×10⁻⁴) = 2.0 × 10¹¹ Pa. The 0.50 mm stretch is written, not drawn: it is 0.02% of 2.5 m. Steel-like Y, original numbers — not a textbook scan.

How it works

  1. Run one Hooke or one YThe case.
  2. A second only as a checkOptional.
  3. StopThis class.
80 N on 2×10⁻⁴ m² is a stress of
  1. 4×10⁵ N/m²
  2. 80 N
  3. 2×10⁻⁴

F/A, not F alone.

Notes

  • Mapped to the official NCERT chapter “Mechanical Properties of Solids”. Original teaching only — no textbook sentences.
  • Science here is Physics, Chemistry and Biology ideas at this class, never a language or social-science chapter.

Formulas

  • stress=F/A
  • strain=ΔL/L
  • Y=stress/strain (linear)

Recap

Hold these pegs from the official chapter “Mechanical Properties of Solids”. The wording is ExamMaster’s teaching, not a textbook recap.

Stress and strain
Stress is force over area; strain is change-in-size over original size.
Hooke’s law
Hooke’s law (school elastic): stress ∝ strain, so F ∝ ΔL, or stress = Y × strain with Y the taught modulus, in the linear range.
Stress-strain curve
A stress–strain curve is a graph: linear start (Hooke), then a taught yield/break if named.
Elastic moduli
Elastic moduli: Young’s Y = (F/A)/(ΔL/L), shear, bulk — as taught.
Applications of elastic behaviour of materials
Applications: a beam that sags, a cable that stretches, a taught safety-margin — the heading is “use the modulus to size ΔL”, not a construction-site tour.
A definition is a test you can run
Stress / Hooke is a test: F/A, ΔL/L, or the linear link.

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