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# Fundamentals of Physics Chapter 12 Solutions: Equilibrium and Elasticity

Halliday Resnick & Walker Fundamentals of Physics Volume 1 Solutions for Chapter 12 ‘Equilibrium and Elasticity’ are created by Physics experts at Instasolv to help you build a strong foundation for JEE. This chapter of Resnick Halliday Walker discusses the forces that remain zero and keep a building or body stationary. Whatever constructions the humans make are supposed to be at rest even if the forces act on them. For example, a building needs to be stable even if the gravitational and wind force acts on it. This chapter will teach you about what mainly allows an object to be stable even if a number of forces are acting on it.

Equilibrium and Elasticity in Resnick Halliday and Walker Physics book help you in understanding the two stability aspects, the equilibrium of the torques and forces that act on rigid objects and the elasticity of the nonrigid objects. Resnick Halliday and Walker Fundamentals of Physics Volume 1 Solutions for Chapter 12 contains a total of 88 questions on topics like equilibrium, the centre of gravity, elasticity, stress, tension, and compression. You will find stepwise solutions along with proper reasoning that will help you understand the chapter thoroughly.

Instasolv is a team of proficient teachers and experts from the field of science who work dedicatedly to solve all your queries. Practice all the questions given in Equilibrium and Elasticity of Halliday Resnick & Walker Fundamentals of Physics for JEE and you will be able to ace the exam easily. The topics covered in this chapter will also be helpful in Class 11 and Class 12 Physics exam preparation.

## Important Topics Covered Under Resnick Halliday & Walker Fundamentals of Physics Volume 1 Solutions Chapter 12: Equilibrium and Elasticity

Equilibrium

In order to understand the concept of equilibrium, let us have a look at an example:

Consider some objects like a book that rests on a table, the rotating blades of a ceiling fan, the wheel of a bicycle travelling along the straight path at a constant speed.

The linear momentum of the centre of mass and the angular momentum about its centre of mass is constant. Such objects are said to be in equilibrium. Thus, there are two requirements for an object to be in equilibrium:

1. Its angular momentum must be constant.
2. Its linear momentum must be constant.

Static Equilibrium

A rigid body that stays at rest is said to be in static equilibrium. In this case, all the external forces that act on the body are zero. Also, the static equilibrium tells that the vector sum of external torque that acts on a body is zero. In the chapter, you will understand the concept of static equilibrium with many examples.

The Center of Gravity

The gravitational force that acts on an entire body is the vector sum of gravitational force that acts on the individual atoms of the same body.  Instead of measuring all those individual gravitational force acting on the body, you can conclude that:

The gravitational force on a body effectively acts at a single point which is known as the centre of gravity of the body.

Here, the word effectively denotes that the net force and the net torque acting on the body would never change.

Elasticity

Whenever a lot of atoms combine together in order to form a solid like an iron nail, they set themselves in an equilibrium position and that too in a three-dimensional pattern. In this pattern, the atoms are arranged in a well-defined equilibrium distance from its neighbours. The interatomic forces hold together the atoms eventually making the lattice rigid. This is the reason why the objects like ladders, tables are perfectly rigid.

A solid changes its dimension in three ways:

• Tension and Compression
• Shearing
• Hydraulic Stress

Stress refers to the deforming force per unit area that produces strain. The stress and strain are proportional. This proportionality constant is known as the modulus of elasticity.

Tension and Compression

The stress is defined as F/A, where F is the magnitude of force applied perpendicular to the area of the object. The strain is the dimensionless quantity L/L, where L is the fractional change in the length of the specimen. This topic will tell you about Young’s Modulus in the chapter.

Shearing

Shearing refers to the deformation of a material substance in which the parallel internal surfaces slide one another. In the case of shearing as well, the stress is the force per unit area but the force lies in the plane of the area and is not perpendicular to the object. This topic is going to detail everything about shearing and shear modulus.

Hydraulic Stress

Hydraulic stress refers to the measurement of internal force per unit area that acts on the liquids. In the chapter, you will study about bulk modulus that will help you to calculate the hydraulic compression or the hydraulic stress.

### Exercise-wise Discussion of Halliday Resnick & Walker Fundamentals of Physics Volume 1 Solutions Chapter 12: Equilibrium and Elasticity

Module 1: Equilibrium

This module has only one question based on equilibrium. In this question, you need to find the coordinates of the centre of mass and gravity of the six particle systems.

Module 2: Some Examples of Static equilibrium

This module has around 41 questions in which you need to find out the magnitude or direction of the force that either breaks a window or pulls a ladder down, the tension that pulls a rope or in the cable that supports an object of heavy mass, the mass of the object, etc.

Module 3: Elasticity

Module 3 contains 9 questions that test your skills on topics like shear stress, vertical deflection, young’s modulus, yield strength, kinetic energy, the amount of work done, and other topics.