Modulus of rigidity

Modulus of rigidity 

Introduction 

This article will discuss the concept of modulus of rigidity and its formula, and  We will discuss the modulus of rigidity formula in detail and solve examples. 

Define modulus of rigidity 

1. Shear modulus refers to the ratio of shear stress to the corresponding shear strain. Shear modulus is also called the modulus of rigidity. 
2. Shear stress can be defined as any force that causes material deformation by slippage along a plane. It can also be described as the internal resistance force induced in a body in response to any deformation caused by an external force. Because of this internal resistance, the body tries to regain its original shape. 
3. On the other hand, shear strain is defined as the ratio of relative displacement of any layer to its perpendicular distance from a fixed layer.
4. According to the principle of modulus of rigidity, all bodies are not perfectly rigid, and when an external force is applied to them, they can bend, compress, and stretch. However, when a body gets deformed due to external force, its internal resisting force tries to regain its original form. This internal resisting force induced to regain the original shape per unit area of the body is called stress. 
5. The SI unit of the shear modulus is N/m2 or Pascal (Pa), and the shear modulus is denoted by the letter G.  It is usually expressed in gigapascals(GPa).

The formula for Modulus of Rigidity 

G represents the modulus of rigidity or shear modulus. 

Shear modulus formula – G = shearing stress shearing strain

Shear Stress:

And Shear Strain:

So Modulus of rigidity can also be expressed as:

Or 

S = G ×  

The SI unit of shear modulus is  N/m2 or Pascal (Pa).

Modulus of rigidity solved examples. 

Example 1- Find the modulus of rigidity of a material on which a tangential force of 2300 N is applied. The surface area of the material is 3 10-6 m2 and is 0.2 m away from the fixed face. The force produces a shift of 7mm of the upper surface concerning the bottom. 

Solution- From the statement mentioned above, we can gather the following information- 

F = 2300 N 

Surface area (A) = 3 10-6 m2

Perpendicular distance of slipping plane from the fixed plane  = 0.2 m 

The relative displacement of slipping plane  △x = 7 mm = 0.007 m 

Modulus of rigidity : 

Putt all the values in the SI unit 

Modulus of rigidity:  G = 23003 10-60.0070.2

Modulus of rigidity = 2300 ×0.2 0.007 × 3 10-6

Modulus of rigidity = 2.191010  N/m2

Conclusion 

With this, we conclude our article on the modulus of rigidity. We hope to clarify and add to your knowledge on the modulus of rigidity. For more related articles on the mechanical properties of solid and other class 11 physics topics, visit Unacademy. Unacademy is India’s leading online learning platform. 

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