[amp_mcq option1=”$${\text{E}} = 3{\text{K}}\left( {1 – \frac{2}{{\text{m}}}} \right)$$” option2=”$${\text{E}} = 2{\text{N}}\left( {1 + \frac{1}{{\text{m}}}} \right)$$” option3=”$$\frac{3}{2}{\text{K}}\left( {1 – \frac{2}{{\text{m}}}} \right) = {\text{N}}\left( {1 + \frac{1}{{\text{m}}}} \right)$$” option4=”All the above” correct=”option4″]
The correct answer is D. All the above.
The modulus of elasticity (E) is a measure of how difficult it is to stretch or compress a material. The modulus of rigidity (N) is a measure of how difficult it is to shear a material. The bulk modulus (K) is a measure of how difficult it is to compress a material in all directions. The Poisson ratio (μ) is a measure of how much a material stretches in the transverse direction when it is stretched in the longitudinal direction.
The following relationships hold good for a linear elastic material:
- E = 3K(1 – 2μ)
- E = 2N(1 + μ)
- 3K(1 – 2μ) = N(1 + μ)
Therefore, all of the options are correct.