Physics · Class 11 Science
Ch 8Mechanical Properties of Solids — Class 11 Physics, concept-first.
In Chapter 6, we studied the rotation of bodies and saw that motion depends on how mass is distributed within the body. That analysis was restricted to rigid bodies — objects that do not change shape under any force.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Youngs Modulus
When you pull on a rubber band, it stretches easily. When you pull on a steel rod of the same size, it barely moves.
Most relevant Q&A
- A structural steel rod has a radius of 10 mm and a length of 1.0 m. A 100 kN force stretches it along its length. Calculate (a) stress, (b)…Preview
- A copper wire of length 2.2 m and a steel wire of length 1.6 m, both of diameter 3.0 mm, are connected end to end. When stretched by a load,…Preview
- In a human pyramid in a circus, the entire weight of the balanced group is supported by the legs of a performer who is lying on his back (as…Preview
- A square lead slab of side 50 cm and thickness 10 cm is subject to a shearing force (on its narrow face) of $9.0 \times 10^{4}\ \text{N}$. T…Preview
- A steel wire of length 4.7 m and cross-sectional area $3.0 \times 10^{-5}\ \text{m}^{2}$ stretches by the same amount as a copper wire of le…Free
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
In Chapter 6, we studied the rotation of bodies and saw that motion depends on how mass is distributed within the body.
Stress and Strain
When you apply a force to a solid object, the object does not remain completely unchanged. It deforms — its shape or size changes, at least a little.
Hooke's Law
When a solid is deformed by an external force, the atoms or molecules are displaced from their equilibrium positions.
Stress-strain Curve
When a solid is subjected to a deforming force, it undergoes a change in shape or size. The relationship between the stress (the internal restoring force per unit area) and the strain (the relative de…
Elastic Moduli
The textbook introduces three distinct moduli, each corresponding to a specific type of strain:
Young's Modulus
3 QWhen a solid is stretched, compressed, or sheared, it deforms. The elastic modulus is the number that tells us how stiff the material is — how much stress it takes to produce a given strain.
+−Worked Examplesi1 question
+−Worked Examplesi1 question
Shear Modulus
When a solid is subjected to a force parallel to one of its faces while the opposite face is held fixed, the shape of the solid changes without any change in volume.
Bulk Modulus
When a solid is subjected to a uniform pressure from all sides — like a cube being squeezed equally on every face — the volume changes but the shape remains the same.
Poisson's Ratio
When you stretch a rubber band lengthwise, you notice it also becomes thinner. This isn't a coincidence — it's a fundamental property of how solids deform.
Elastic Potential Energy in a Stretched Wire
When a wire is stretched, the work done by the deforming force is stored inside the material as elastic potential energy.
Applications of Elastic Behaviour of Materials
The theory of elasticity is not just an abstract set of formulas — it is the engineering backbone of every structure you see around you.
Summary
- Stress is the internal restoring force per unit area: . Strain is the fractional change in dimension: (longitudinal), (volumetric), or (shear).
Points to Ponder
1. When a wire hangs from a ceiling with a weight attached at the bottom, the ceiling pulls upward on the wire with a force equal to (Newton’s third law).
Exercises
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- 8.1A steel wire of length 4.7 m and cross-sectional area $3.0 \times 10^{-5}\ \text{m}^{2}$ stretches by the same amount as a copper wire of le…Free
- 8.2Figure 8.9 shows the strain-stress curve for a given material. What are (a) Young's modulus and (b) approximate yield strength for this mate…Free
- 8.3The stress-strain graphs for materials A and B are shown in Fig. 8.10. ![Fig 8.10 -- Stress-strain graphs for materials A and B, drawn to th…Free
- 8.4Read the following two statements below carefully and state, with reasons, if it is true or false. (a) The Young's modulus of rubber is grea…Preview
- 8.5Two wires of diameter 0.25 cm, one made of steel and the other made of brass are loaded as shown in Fig. 8.11. The unloaded length of steel…Preview
- 8.6The edge of an aluminium cube is 10 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to t…Preview
- 8.7Four identical hollow cylindrical columns of mild steel support a big structure of mass 50,000 kg. The inner and outer radii of each column…Preview
- 8.8A piece of copper having a rectangular cross-section of $15.2\ \text{mm} \times 19.1\ \text{mm}$ is pulled in tension with 44,500 N force, p…Preview
- 8.9A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed $10^{8}\ \text{N m}^{-2}$,…Preview
- 8.10A rigid bar of mass 15 kg is supported symmetrically by three wires each 2.0 m long. Those at each end are of copper and the middle one is o…Preview
- 8.11A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of…Preview
- 8.12Compute the bulk modulus of water from the following data: Initial volume = 100.0 litre, Pressure increase = 100.0 atm ($1\ \text{atm} = 1.0…Preview
- 8.13What is the density of water at a depth where pressure is 80.0 atm, given that its density at the surface is $1.03 \times 10^{3}\ \text{kg m…Preview
- 8.14Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of 10 atm.Preview
- 8.15Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of $7.0 \times 10^{6}\ \te…Preview
- 8.16How much should the pressure on a litre of water be changed to compress it by 0.10%?Preview
Exemplar Problems
Higher-order thinking / exemplar-style practice problems.
+−Show 29 questionsHide questions29 questions
- Q1Modulus of rigidity of ideal liquids is (a) infinity. (b) zero. (c) unity. (d) some finite small non-zero constant value.Free
- Q2The maximum load a wire can withstand without breaking, when its length is reduced to half of its original length, will (a) be double. (b) b…Free
- Q3The temperature of a wire is doubled. The Young's modulus of elasticity (a) will also double. (b) will become four times. (c) will remain sa…Free
- Q4A spring is stretched by applying a load to its free end. The strain produced in the spring is (a) volumetric. (b) shear. (c) longitudinal a…Preview
- Q5A rigid bar of mass $M$ is supported symmetrically by three wires each of length $l$. Those at each end are of copper and the middle one is…Preview
- Q6A mild steel wire of length $2L$ and cross-sectional area $A$ is stretched, well within the elastic limit, horizontally between two rigid pi…Preview
- Q7A rectangular frame is to be suspended symmetrically from overhead supports by two strings of equal length, each string tied to one of the t…Preview
- Q8Consider two cylindrical rods of identical dimensions, one of rubber and the other of steel. Both the rods are fixed rigidly at one end to t…Preview
- Q9The stress-strain graphs (stress on the vertical axis, strain on the horizontal axis, both drawn to the same scale) for two materials (i) an…Preview
- Q10A wire is suspended from the ceiling and stretched under the action of a weight $F$ suspended from its other end. The force exerted by the c…Preview
- Q11A rigid rod of length $l$ and negligible mass hangs horizontally from the ceiling, supported at its two ends by two vertical wires of equal…Preview
- Q12For an ideal liquid (Note: more than one of the given options may be correct.) (a) the bulk modulus is infinite. (b) the bulk modulus is zer…Preview
- Q13A copper and a steel wire of the same diameter are connected end to end. A deforming force $F$ is applied to this composite wire which cause…Preview
- Q14The Young's modulus for steel is much more than that for rubber. For the same longitudinal strain, which one will have greater tensile stres…Preview
- Q15Is stress a vector quantity?Preview
- Q16Identical springs of steel and copper are equally stretched. On which, more work will have to be done?Preview
- Q17What is the Young's modulus for a perfect rigid body?Preview
- Q18What is the Bulk modulus for a perfect rigid body?Preview
- Q19A wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$, its length incre…Preview
- Q20A steel rod ($Y = 2.0 \times 10^{11}$ Nm$^{-2}$; and $\alpha = 10^{-5}\,{}^{\circ}\text{C}^{-1}$) of length 1 m and area of cross-section 1…Preview
- Q21To what depth must a rubber ball be taken in deep sea so that its volume is decreased by 0.1%. (The bulk modulus of rubber is $9.8 \times 10…Preview
- Q22A truck is pulling a car out of a ditch by means of a steel cable that is 9.1 m long and has a radius of 5 mm. When the car just begins to m…Preview
- Q23Two identical solid balls, one of ivory and the other of wet-clay, are dropped from the same height on the floor. Which one will rise to a g…Preview
- Q24Consider a long steel bar of uniform cross-sectional area $A$ (measured perpendicular to its length) placed under a tensile stress by two eq…Preview
- Q25(a) A steel wire of mass $\mu$ per unit length with a circular cross section has a radius of 0.1 cm. The wire is of length 10 m when measure…Preview
- Q26A steel rod of length $2l$, cross sectional area $A$ and mass $M$ is set rotating in a horizontal plane about an axis passing through the ce…Preview
- Q27An equilateral triangle ABC is formed by two Cu rods AB and BC and one Al rod. It is heated in such a way that temperature of each rod incre…Preview
- Q28In nature, the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or c…Preview
- Q29A stone of mass $m$ is tied to an elastic string of negligble mass and spring constant $k$. The unstretched length of the string is $L$ and…Preview