NCERT  ·  Physics  ·  Class XI  ·  Ch.9

Mechanical Properties of Solids
MCQ Master Series

Stress · Strain · Hooke’s Law · Elastic Constants

🔥 50 Questions
⏱ 40 min Suggested
📊 3 Tiers
🗂 6 Topics
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Question Intelligence

Quiz Analytics

A data-driven breakdown of all 50 questions by difficulty, exam origin and topic distribution.

📈 Distribution Overview

50
Total Questions
CBSE Level
26
JEE Main Level
15
JEE Advanced Level
9

🗂 Topic Coverage

Basic Elasticity & Hooke’s Law
20%
Stress–Strain & Moduli (Y, K, G)
32%
Poisson’s Ratio & Relations
12%
Energy in Deformation
16%
Material Behaviour (Ductile etc.)
12%
Design & Fatigue Concepts
8%
26
CBSE Level
15
JEE Main Level
9
JEE Advanced Level
Conceptual Framework

Key Concept Highlights

6 foundational pillars that power every question in this quiz. Understand these, and the answers follow naturally.

📈
Stress–Strain Framework
Normal, shear and volumetric stress vs corresponding strains, with Hooke’s law holding linearly only up to the proportional limit.
🧷
Elastic Constants (Y, K, G, ν)
Young’s modulus, bulk modulus, shear modulus and Poisson’s ratio quantify rigidity, compressibility, shear response and lateral contraction.
📊
Stress–Strain Curve of Solids
Proportional limit, elastic limit, yield point, ultimate stress and breaking point classify ductile vs brittle behaviour and safe working stress.
🔋
Elastic Potential Energy
Energy stored per unit volume \(= \tfrac{1}{2} \sigma \varepsilon\) under linear elasticity, crucial for springs, wires and energy‑absorbing components.
🛠️
Engineering Design & Safety
Factor of safety, elastic fatigue, creep and damping guide how bridges, cables and machine parts are sized below elastic and breaking limits.
🌉
Material Choice in Practice
Steel, copper, rubber etc. differ in Young’s modulus, ductility and plasticity, deciding their use in suspension cables, springs and dampers.
Pedagogical Value

Why MCQs Matter

Multiple-choice questions are not mere guessing games — they are the sharpest diagnostic tool available to a competitive exam aspirant.

~20%

of JEE/NEET mechanics marks tie back to stress–strain and elastic constants

Quick Reference

Important Formula Capsules

10 must-memorise equations that surface repeatedly across CBSE and JEE papers.

Stress
\[ \sigma = \dfrac{F}{A} \]
Strain
\[ \varepsilon = \dfrac{\Delta L}{L} \]
Hooke’s Law
\[ \sigma = Y\,\varepsilon \]
Young’s Modulus
\[ Y = \dfrac{\text{normal stress}}{\text{longitudinal strain}} \]
Bulk Modulus
\[ K = -\dfrac{\Delta P}{\Delta V / V},\quad B = \dfrac{1}{K} \]
Shear Modulus
\[ G = \dfrac{\text{shear stress}}{\text{shear strain}} \]
Poisson’s Ratio
\[ \nu = -\dfrac{\text{lateral strain}}{\text{longitudinal strain}} \]
Elastic Energy/Volume
\[ u = \dfrac{1}{2}\sigma\varepsilon = \dfrac{1}{2}Y\varepsilon^{2} \]
Spring Energy
\[ U = \dfrac{1}{2}k x^{2} \]
Moduli Relation
\[ Y = 3K\left(1 - 2\nu\right) = 2G\left(1 + \nu\right) \]
Learning Outcomes

What You Will Learn

By completing this quiz set you will have exercised all the following competencies.

01 Identify which elastic constant (Y, K, G) is relevant in a given deformation situation
02 Interpret stress–strain curves to locate elastic limit, yield point and breaking stress
03 Use Hooke’s law to relate stress, strain and extension for wires and rods
04 Compute elastic energy stored in a stretched wire or spring and relate it to design limits
05 Compare materials on the basis of rigidity, elasticity, ductility and plasticity
06 Apply relations between Y, K, G and Poisson’s ratio to mixed‑constant problems
07 Recognise practical issues like elastic fatigue, creep and factor of safety in engineering structures
Exam Preparation

Strategy & Preparation Tips

5 evidence-based strategies to maximise your score in CBSE Boards and JEE.

Step 01
Lock in Definitions
Be precise with definitions of stress, strain, Young’s modulus, bulk modulus, shear modulus and Poisson’s ratio — many one‑liners target wording.
Step 02
Sketch the Curve
Practise the full stress–strain curve and label key points; several MCQs ask “which region” or “which point” corresponds to a given description.
Step 03
Relate the Constants
Memorise and derive \(Y = 3K(1-2\nu) = 2G(1+\nu)\); mixed‑constant questions and “which quantity is independent of” rely on these links.
Step 04
Energy & Design View
Solve problems on elastic energy per unit volume and working stress; these link conceptual questions on safety factors and choice of material.
Step 05
Concept Traps Practice
Pay special attention to conceptual traps: unitless strain, sign in bulk modulus, incompressible limit (\(\nu \to 0.5\)), and what changes or stays same when a wire is cut or diameter altered.

Ready to Test Your Mastery?

50 questions  ·  Elapsed timer  ·  Instant scored results

⚡ Begin Mechanical Properties of Solids Quiz
🎯 Knowledge Check

Physics — MECHANICAL PROPERTIES OF SOLIDS

50 Questions Class 11 MCQs
1
Which property of a material enables it to regain its original shape after deformation?
2
The ratio of stress to strain within elastic limit is called:
3
Which of the following quantities has no unit?
4
The SI unit of stress is:
5
Hooke’s law is valid up to:
6
Young’s modulus is defined as:
7
A material having large Young’s modulus is:
8
The negative sign in bulk modulus formula indicates:
9
Which stress acts on a body when it is twisted?
10
Poisson’s ratio is the ratio of:
11
The value of Poisson’s ratio for an incompressible material is:
12
Which of the following materials is most elastic?
13
Elastic potential energy stored in a stretched wire depends on:
14
The expression for elastic potential energy of a wire is:
15
Stress–strain curve beyond elastic limit shows:
16
The area under stress–strain curve up to elastic limit represents:
17
Which material is best suited for suspension cables?
18
Which of the following increases the elongation of a wire?
19
The phenomenon of weakening of elastic property due to repeated loading is:
20
Hydraulic brakes work on the principle of:
21
If stress is doubled within elastic limit, strain becomes:
22
The slope of stress–strain graph in elastic region gives:
23
Which quantity decides rigidity of a solid?
24
A wire of length \(L\) is cut into two equal parts. Young’s modulus will:
25
Energy stored per unit volume of wire is called:
26
Which factor does not affect elongation of a wire?
27
In which case shear modulus is involved?
28
The ratio of bulk modulus to Young’s modulus depends on:
29
If Poisson’s ratio is zero, the material:
30
The restoring force in elastic deformation arises due to:
31
For maximum elastic energy storage, a material should have:
32
The stress at breaking point is called:
33
Which curve best represents Hooke’s law?
34
Creep is observed when:
35
Elastic behavior is most important in:
36
If the diameter of a wire is doubled, its elongation becomes:
37
The unit of bulk modulus is:
38
Which material shows maximum plasticity?
39
Stress–strain curve is useful to find:
40
Elasticity is a:
41
A wire obeys Hooke’s law if:
42
Which of the following has the highest bulk modulus?
43
The elastic energy stored in a spring is maximum when:
44
The phenomenon responsible for damping in materials is:
45
Engineering structures are designed with:
46
Which elastic constant relates volume change with pressure?
47
If a material has very small Young’s modulus, it is:
48
Elastic fatigue is dangerous because:
49
Which graph represents elastic potential energy vs extension?
50
Knowledge of elastic constants is essential mainly for:

Frequently Asked Questions

Mechanical properties describe how solids respond to applied forces, such as stretching, compressing, bending, or twisting.

Elasticity is the property of a material by which it regains its original shape and size after removal of the deforming force.

Elastic limit is the maximum stress up to which a material returns completely to its original dimensions when the force is removed.

Stress is the internal restoring force per unit area developed inside a material when an external force is applied.

Strain is the fractional change in dimension (length, volume, or shape) produced due to stress.

Stress = Force / Area

Strain = Change in dimension / Original dimension

Hooke’s law states that stress is directly proportional to strain within the elastic limit of a material.

Young’s modulus is the ratio of longitudinal stress to longitudinal strain.

Y = (Longitudinal stress) / (Longitudinal strain)

It indicates that the material is stiff and undergoes very little deformation under stress.

Bulk modulus is the ratio of volume stress to volume strain.

K = -?P / (?V / V)

Because an increase in pressure causes a decrease in volume.

Shear modulus is the ratio of shear stress to shear strain.

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