We are sharing this article on Modulus of Rigidity, wherein we have included complete notes on types of Modulus. Carefully go through the detailed notes to understand this concept, as it will help you prepare for the upcoming JEE Main, BITSAT, VITEEE exams. Moreover, you can also make short notes on Modulus of Rigiditybased to revise during the exam time.
Modulus of Rigidity
A body is said to be rigid if it has a definite shape and size. The solid bodies which we see around us are not perfectly rigid. They can be compressed, stretched and bent when applied with an external force.
When an external force is applied, the objects get deformed. Some objects tend to regain their original shapes. The internal force that is acting per unit area of the body to regain their original shape is known as Stress. The ratio of the change in any dimension produced in the body to the original dimension is called Strain.
A relationship has been established between stress and strain which is known as Modulus of Elasticity. It is defined as the ratio of stress to the corresponding strain, within the elastic limit.
The SI unit of elasticity is Nm-2 and its dimensions are [ML-1T-2].
There are three types of Modulus of elasticity corresponding to the three types of strain (Longitudinal, Volumetric, and Shear).
- Young’s Modulus
- Bulk Modulus
- Shear Modulus
Modulus of Rigidity types are described below in detail, go through the notes to understand the given concept.
Young’s Modulus of Elasticity
Within the elastic limit, the ratio of longitudinal stress to the longitudinal strain is called Young’s Modulus of Elasticity.
As shown in the figure, suppose a wire of length l and cross-section area A suffers an increase in length Δl under a force F acting along its length l. Then Young’s modulus is given by
If l = 1m, A = 1m2 and Δl =1m then Y = F
Thus, Young’s Modulus of elasticity is equal to the Force required to extend a wire of unit length and unit area of cross-section by a unit amount, i.e., the force required to double the length of the wire.
Check Related Articles – JEE Main Physics Sample Paper ,JEE Main Chemistry Sample Paper, JEE Main Numerical Sample Paper
Bulk Modulus of Elasticity
Within the elastic limit, the ratio of normal stress to the volumetric strain is called bulk modulus of elasticity.
Consider a body of surface area A and volume V. suppose a force F acts uniformly over the whole surface of the body and it decreases the volume by dV. The bulk modulus of elasticity is given by
The SI unit of bulk modulus is Nm-2 or Pascal (Pa).
It can be defined as the ratio of tangential stress to shear strain within the elastic limit.
To understand this, consider a rectangular block whose lower face is fixed and a tangential force F is applied over its upper face of area A. an equal and opposite force F comes into play on its lower fixed face. The two equal and opposite forces form a couple that exerts a torque. As the lower face of the block is fixed, the couple shears the block into a parallelopiped by displacing its upper face through distance AA’ = Δx. Let AB = DC = x and ∠ABA’ = θ.
The SI unit of shear modulus is also Nm-2
Summarized Notes On Modulus Of Rigidity
Check the summarized notes on Modulus of Rigidity. You can also make short notes of these to prepare quickly for the engineering entrance exam you are preparing for.
- Stress is the internal force applied by the body in response to the external force to regain its shape.
- The deformation occurred because of the force is known as strain
- Modulus of elasticity establishes a relationship between stress and strain
- The ratio of stress to strain within the elastic limit is known as modulus of elasticity.
Our experts have tried to cover the concept of Modulus of Rigidity in the above article. If you have any query then put that in the comment section. Have a glance at the related articles to ace your exam preparations Bulk Modulus, Properties of Materials, and Banking of Roads
All the Best for your Exams!
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