If E, N, K and $$\frac{1}{{\text{m}}}$$ are modulus of elasticity, modulus of rigidity. Bulk modulus and Poisson ratio of the material, the following relationship holds good A. $${\text{E}} = 3{\text{K}}\left( {1 – \frac{2}{{\text{m}}}} \right)$$ B. $${\text{E}} = 2{\text{N}}\left( {1 + \frac{1}{{\text{m}}}} \right)$$ C. $$\frac{3}{2}{\text{K}}\left( {1 – \frac{2}{{\text{m}}}} \right) = {\text{N}}\left( {1 + \frac{1}{{\text{m}}}} \right)$$ D. All the above

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.