# Study Notes for Class 11 Physics Chapter 9 Mechanical Properties of Solids

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### Introduction

All the rigid bodies are to some extent elastic. This means that their dimensions can be changed by pulling, pushing, twisting or by compressing them. e.g. When a helical spring is gently pulled at its both ends, the length of helical spring increases slightly. When we remove the forces applied at the ends of spring, it regains its original size and shape. Similarly when a rubber cord is pulled at both the ends, its length increases as long as it is pulled. As soon as the forces applied at the two ends of rubber cord are removed, rubber cord regains its original size and shape.

When a body is subjected to a set of balanced forces; which do not cause any type of motion, produce change in size, shape or both. Some bodies undergo change in dimensions (size, shape or both) easily, while some bodies are reluctant to undergo any change in dimensions. Some bodies show permanent change in their size, shape or both, after removal of applied force, whereas some bodies preserve their original size, shape or both after removal of applied force.

### Origin of elasticity

Solid consists of atoms and molecules situated at definite positions in equilibrium state. When a force is applied to a body the atoms in a body are displaced from their equilibrium positions. Internal elastic forces are set up within body, which try to restore the equilibrium positions of atoms. The applied force and internal elastic force are numerically equal in deformed state. When external applied force is removed, internal elastic force is responsible for maintaining the original dimensions (i.e. size, shape or both) of body. In other words solid body is said to possess the property of elasticity of volume and elasticity of shape.

The property by virtue of which material bodies regain their original dimensions (size, shape or both) after removal of deforming force is called elasticity.

Perfectly elastic body: Quartz

### Plasticity:

Plasticity is the property of a material to undergo a permanent deformation even after removal of external deforming forces.

The bodies which do not regain their original dimensions (size, shape or both) after removal of deforming forces are called plastic bodies. These bodies can be deformed to a large extent by a small deforming force. As such no body is perfectly elastic or perfectly plastic. Clay, Plasticine and Putty are the examples of plastic bodies.

Perfect Plasticity exhibited by certain material is its property to undergo irreversible deformation without any increase in load. Putty is an example of perfectly plastic body.

### Deformation:

Most of the bodies can be deformed by application of suitable external force. The change in size, shape or both of a body arising due to external force is called deformation. The force which is responsible for deformation of body is called deforming force. In general,

deformation ∝ deforming force

There are many ways in which deformation may take place.

Deformation may be

• Change in length in case of wire and cord.
• Change in the volume of a body
• Change in the shape of body

When deformation of body take place, the body is said to be in strained condition or deformed state. When a rubber cord or a metal wire is stretched, its length increases. The wire regains its original length after removal of applied force. When an inflated volley ball bladder is pressed by hands, there is change in its shape and volume. As soon as we remove our hands, the rubber bladder of volley ball, regains its original volume and shape.

In the deformed state, the applied force is numerically equal to internal elastic restoring force within a body, but in opposite direction.

Thus deformation produced in a body is due to change in relative positions of the molecules within a body, due to applied deforming force.

### Definition of Stress and Strain:

The elastic properties of a body are described in terms of concepts like stress and strain.

Stress is defined as internal elastic restoring force per unit cross sectional area of body.

In equilibrium, the applied force and internal elastic restoring force are numerically equal, however they are oppositely directed. Hence,

Stress is defined as applied force per unit cross sectional area of body.

Thus,

The S.I. unit of stress is N/m2 or Pa and the c.g.s. unit of stress is dyne/cm2.

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