Match the following A. Youngs modulus 1. Shear strain B. Modulu
Match the following
| A. Youngs modulus | 1. Shear strain |
| B. Modulus of rigidity | 2. Normal strain |
| C. Bulk modulus | 3. Transverse strain |
| D. Poisson’s ratio | 4. Volumetric strain |
A. A – 1, B – 2, C – 3, D - 4
B. A – 2, B – 1, C – 3, D - 4
C. A – 2, B – 1, C – 4, D - 3
D. A – 1, B – 2, C – 4, D - 3
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
Explanation:
Young's modulus:
- The mechanical property of a material to withstand the compression or the elongation with respect to its length of linear elastic solids like rods, wires etc is called Young's modulus.
- It is also referred to as the Elastic Modulus or Tensile Modulus
- It gives us information about the tensile elasticity of a material (ability to deform along an axis).
The formula of young modulus is given as,
\(E =\frac {Normal ~stress}{Normal ~strain}= \frac {\sigma}{\epsilon}\)
where E is Young’s modulus in Pa, 𝞂 is the uniaxial stress in Pa,ε is the Normal strain or proportional deformation.
Modulus of rigidity:
- It is also known as shear modulus.
- It is the mechanical property of a material due to which it withstand shear stress and resist torsion.
- It is the ratio of shear stress to the corresponding shear strain within the elastic limit. This is denoted by G and given by.
\(\therefore {G} = \frac{{Shear\;stress}}{{Shear\;strain}} = \frac{\tau }{\phi }\)
Bulk modulus:
- It is the mechanical property of a material due to which it resist the change in volume due to external pressure or equal stress in all directions.
- The concept of bulk modulus can be used in case of Hydrostatic loading.
- It is defined as the ratio of normal stress to the volumetric strain and denoted by 'K' and given by,
\(K = \frac {Normal ~stress}{Volumetric ~strain}= \frac {\sigma }{\epsilon _v}\)
Poisson's ratio:
- When the body is loaded within its elastic limit, the ratio of lateral or transverse strain and linear or longitudinal strain is constant. This constant is known as Poisson's ratio. It is given by,
\({\rm{μ }} = \frac{{{-\rm{Lateral\;strain}}}}{{{\rm{Linear\;strain}}}}\)
Relations between Youngs modulus(E), Shear modulus(G), Bulk modulus(K) and Poisson's ratio(μ)
- E = 2G (1 + μ)
- E = 3K (1 – 2μ)
- \({\bf{E}} = \frac{{9{\bf{KG}}}}{{3{\bf{K}}~ + \;{\bf{G}}}}\)
- \({\bf{\mu }} = \frac{{3{\bf{K}}~ - ~2{\bf{G}}}}{{2{\bf{G}} ~+ ~6{\bf{K}}}}\)
