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The dimensions of shear modulus of rigidity are
- a)M1L1T−2
- b)M1L1T−1
- c)ML2T2
- d)ML−1T−2
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The dimensions of shear modulus of rigidity area)M1L1T−2b)M1L1T&...
Understanding Shear Modulus of Rigidity
Shear modulus, also known as the modulus of rigidity, is a measure of a material's ability to resist shear deformation. The dimensions of shear modulus can be derived from the relationship between stress and strain.
Definition of Shear Modulus
- Shear modulus (G) is defined as the ratio of shear stress to shear strain.
- Mathematically, G = Shear Stress / Shear Strain.
Dimensions of Shear Stress
- Shear stress (τ) is defined as force (F) per unit area (A).
- Dimensions of force: M1L1T-2 (mass x acceleration).
- Dimensions of area: L2.
- Therefore, the dimensions of shear stress are:
τ = F/A = (M1L1T-2) / (L2) = M1L-1T-2.
Dimensions of Shear Strain
- Shear strain (γ) is the ratio of the change in the shape of the material to its original shape.
- It is a dimensionless quantity, so its dimensions are 1.
Calculating Dimensions of Shear Modulus
- Using the definitions, we can find the dimensions of shear modulus (G):
G = τ / γ = (M1L-1T-2) / 1 = M1L-1T-2.
Conclusion
- The correct dimensions of shear modulus of rigidity are:
ML-1T-2 (option D).
This aligns with the fundamental principles of mechanics and material science, validating the choice. Understanding these dimensions is crucial for applications in engineering and physics.
Shear modulus, also known as the modulus of rigidity, is a measure of a material's ability to resist shear deformation. The dimensions of shear modulus can be derived from the relationship between stress and strain.
Definition of Shear Modulus
- Shear modulus (G) is defined as the ratio of shear stress to shear strain.
- Mathematically, G = Shear Stress / Shear Strain.
Dimensions of Shear Stress
- Shear stress (τ) is defined as force (F) per unit area (A).
- Dimensions of force: M1L1T-2 (mass x acceleration).
- Dimensions of area: L2.
- Therefore, the dimensions of shear stress are:
τ = F/A = (M1L1T-2) / (L2) = M1L-1T-2.
Dimensions of Shear Strain
- Shear strain (γ) is the ratio of the change in the shape of the material to its original shape.
- It is a dimensionless quantity, so its dimensions are 1.
Calculating Dimensions of Shear Modulus
- Using the definitions, we can find the dimensions of shear modulus (G):
G = τ / γ = (M1L-1T-2) / 1 = M1L-1T-2.
Conclusion
- The correct dimensions of shear modulus of rigidity are:
ML-1T-2 (option D).
This aligns with the fundamental principles of mechanics and material science, validating the choice. Understanding these dimensions is crucial for applications in engineering and physics.
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Community Answer
The dimensions of shear modulus of rigidity area)M1L1T−2b)M1L1T&...
The dimensions of the shear modulus of rigidity are expressed in terms of mass (M), length (L), and time (T). The correct dimensional formula is:
- M1L-1T-2
This indicates that the shear modulus relates to the ratio of shear stress to shear strain, with units reflecting force per unit area.
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