Lead, as a material used in construction, has E = 15 GPa and K =

SOLUTION

Concept:

Modulus of Elasticity: Modulus of elasticity is a measure of the resistance to the deformation of an object when it is being deformed elastically. It is also known as Young’s Modulus.

Bulk Modulus: Bulk modulus is a measure of the resistance to volumetric compression of an object when it is being compressed volumetrically.

Poisson’s Ratio: Poisson’s ratio is the measure of the effect of an increase in longitudinal dimension (length) to the decrease in lateral dimension (width or diameter).

The relationship between modulus of elasticity (E), bulk modulus (k) and Poisson’s ratio (μ) is given by,

\({\rm{E}} = 3{\rm{k}}\left( {1 - 2{\rm{μ }}} \right)\)

Calculations:

Given, Modulus of elasticity, E = 15 GPa and Bulk modulus, K = 50 GPa.

\(∴ 15 = 3 \times 50 \times \left( {1 - 2{\rm{μ }}} \right)\)

∴ μ = 0.45

∴ Poisson’s Ratio of the material is 0.45.