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Ever been curious about why bridges don't break under weight? Or why does a rubber band expand and come back to shape? Well, the Mechanical Properties of Solids has all the answers! This chapter in the NCERT Class 11 Physics goes deep into the way to let students understand all this.
Mechanical Properties of Solids is a crucial topic in covering fundamental concepts that help explain why objects are attracted to the Earth. If you struggle to grasp the concept of the mechanical properties of solids or solve NCERT textbook questions, Careers360 provides detailed NCERT solutions to assist you in your studies.
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This chapter primarily deals with questions related to elasticity and deformation, making it easier to understand the fundamental concepts, which are crucial in competitive exams such as NEET and JEE Main. The NCERT solutions for Class 11 Physics Chapter 8 help students strengthen their understanding and improve their problem-solving skills.
According to the CBSE Syllabus for the academic year 2025-26, the chapter you previously referred to as Chapter 9, " Physics class 11 Mechanical Properties of Solids, has been renumbered as Chapter 8.
Answer:
Let the Young's Modulus of steel and copper be Y S and Y C respectively.
Length of the steel wire l S = 4.7 m
Length of the copper wire l C = 4.7 m
The cross-sectional area of the steel wire A S =
The cross-sectional area of the Copper wire A C =
Let the load and the change in the length be F and
Since F and
The ratio of Young’s modulus of steel to that of copper is 1.79.
8.2 (a) Figure 8.9 shows the strain-stress curve for a given material. What are (a)
Fig. 8.9
Answer:
Young’s modulus is given as the ratio of stress to strain when the body is behaving elastically.
For the given material
8.2(b)What are approximate yield strength for this material?
Answer:
The Yield Strength is approximately
Fig 8.10
Answer:
As we can see in the given Stress-Strain graphs that the slope is more in the graph corresponding to material A. We conclude that A has a greater Young's Modulus.
8.3(b) Which of the two is the stronger material?
Answer: The material which fractures at higher stress is said to be stronger. As we can see in the given Stress-Strain graphs the stress at which the material fractures is higher in A than that in B we conclude that A is the stronger material.
8.4(a) Read the following two statements below carefully and state, with reasons, if it is true or false.
The Young’s modulus of rubber is greater than that of steel;
Answer:
False: Young's Modulus is defined as the ratio of the stress applied on a material and the corresponding strain that occurs. As for the same amount of pressure applied on a piece of rubber and steel, the elongation will be much lesser in case of steel than that in the case of rubber and therefore the Young's Modulus of rubber is lesser than that of steel.
Answer:
True: As the force acts Normal to the parallel planes in which helical parts of the wire lie, the actual length of the wire would not change but it's shape would. Therefore the amount of elongation of the coil taking place for corresponding stress depends upon the Shear Modulus of elasticity.
Fig 8.11
Answer:
Tension in the steel wire is F 1
Length of steel wire l 1 = 1.5 m
The diameter of the steel wire, d = 0.25 cm
Area od the steel wire,
Let the elongation in the steel wire be
Young's Modulus of steel, Y 1 =
Tension in the Brass wire is F 2
Length of Brass wire l 2 = 1.5 m
Area of the brass wire,
Let the elongation in the steel wire be
Young's Modulus of steel, Y 2 =
Answer:
Edge of the aluminium cube, l = 10 cm = 0.1 m
Area of the face of the Aluminium cube, A = l 2 = 0.01 m 2
Tangential Force is F
Tangential Stress is F/A
Shear modulus of aluminium
Let the Vertical deflection be
Answer:
Inner radii of each column, r 1 = 30 cm = 0.3 m
Outer radii of each column, r 2 = 60 cm = 0.6 m
Mass of the structure, m = 50000 kg
Stress on each column is P
Youngs Modulus of steel is
Answer:
Length of the copper piece, l = 19.1 mm
The breadth of the copper piece, b = 15.2 mm
Force acting, F = 44500 N
Modulus of Elasticity of copper,
Answer:
Let the maximum Load the Cable Can support be T
Maximum Stress Allowed, P = 10 8 N m -2
Radius of Cable, r = 1.5 cm
Answer:
Each wire must support the same load and are of the same length and therefore should undergo the same extension. This, in turn, means they should undergo the same strain.
Answer:
Mass of the body = 14.5 kg
Angular velocity,
The radius of the circle, r = 1.0 m
Tension in the wire when the body is at the lowest point is T
Cross-Sectional Area of wire, A = 0.065 cm 2
Young's Modulus of steel,
Answer:
Pressure Increase, P = 100.0 atm
Initial Volume = 100.0 l
Final volume = 100.5 l
Change in Volume = 0.5 l
Let the Bulk Modulus of water be B
The bulk modulus of air is
The Ratio of the Bulk Modulus of water to that of air is
This ratio is large as for the same pressure difference the strain will be much larger in the air than that in water.
Answer:
Water at the surface is under 1 atm pressure.
At the depth, the pressure is 80 atm.
Change in pressure is
Bulk Modulus of water is
The negative sign signifies that for the same given mass the Volume has decreased
The density of water at the surface
Let the density at the given depth be
Let a certain mass occupy V volume at the surface
Dividing the numerator and denominator of RHS by V we get
The density of water at a depth where pressure is 80.0 atm is
Answer:
Bulk's Modulus of Glass is
Pressure is P = 10 atm.
The fractional change in Volume would be given as
The fractional change in Volume is
Answer:
The bulk modulus of copper is
Edge of copper cube is s = 10 cm = 0.1 m
Volume Of copper cube is V = s 3
V = (0.1) 3
V = 0.001 m 3
Hydraulic Pressure applies is
From the definition of bulk modulus
The volumetric strain is
Volume contraction will be
The volume contraction has such a small value even under high pressure because of the extremely large value of the bulk modulus of copper.
8.16 How much should the pressure on a litre of water be changed to compress it by 0.10%?
Answer:
Change in volume is
Bulk modulus of water is
A pressure of
Note: The answer is independent of the volume of water taken into consideration. It only depends on the percentage change.
1. A 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 of iron. The ratio of their diameters, if each is to have the same tension, is equal to?
Solution:
Hence,
So,
2. What will be the maximum load a wire can withstand without breaking when its length is reduced to half of its original length?
Solution: Stress = force/area
The breaking stress is not dependent on the length, and hence, if the cross-sectional area is changed, it will not affect the breaking force.
3. What happens to the Young’s modulus of elasticity when the temperature of a wire is doubled?
Solution: As we learn,
So as the Young’s modulus increases, elasticity decreases.
4. A spring is stretched by applying a load to its free end. What is the strain produced in the spring?
Solution: The strain produced in a material can be shearing or longitudinal, depending on the type of force applied. In the case of a spring stretched by a load, the shape and length of the spring both change. When a longitudinal strain is produced, the length of the spring increases or decreases in the direction of the applied force.
5. Consider two cylindrical rods of identical dimensions, one of rubber and the other of steel. Both rods are fixed rigidly at one end of the roof. A mass M is attached to each of the free ends at the centre of the rods. Then:
Solution: The steel rod will elongate, without any perceptible change in shape, but the rubber rod will elongate with the shape of the bottom edge tapered to a tip at the centre.
Y steel
Hence,
Understand the Basic Terms and Definitions
Know these key concepts first:
Types: Tensile, Compressive, Shearing
Types: Longitudinal, Volumetric, Shearing
Understand key points of the curve:
Proportional Limit
Elastic Limit
Yield Point
Ultimate Stress
Breaking Point
Know the difference between elastic and plastic behaviour
Choose the Right Formula Based on the Type of Deformation
For stretching/compression:
For volumetric strain under pressure:
For shear deformation:
Concept Name | JEE | NCERT |
Elasticity | ✅ | ✅ |
Stress And Strain | ✅ | ✅ |
Stress Strain Relationship | ✅ | ✅ |
Hooke’s Law | ✅ | ✅ |
Work Done In Stretching A Wire | ✅ | ✅ |
Relation Between Volumetric Strain, Lateral Strain And Poisson’s Ratio | ✅ |
NCERT Solutions for Class 11 Subject-wise
The topics covered in the NCERT book Class 11 physics chapter 9 are
One question may be asked from mechanical properties of solids for JEE Main exam. To practice more questions refer to previous year JEE main papers, NCERT book and NCERT exemplar problems.
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