The correct relation between Modulus of elasticity (E), Shear Modulus (G) and Bulk modulus (K) is:

Question

Question

Answer 1

CONCEPT:

Modulus of elasticity: The quantity which measures the resistance to being deformed elastically when a stress is applied to an object is called modulus of elasticity.
- It is denoted by E.
Shear modulus: The ratio of shear stress to shear strain is called shear modulus.
It is denoted by G.
Bulk modulus: The measure of how resistant a substance is about its compression is called bulk modulus.
- It is the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.
- It is denoted by K.
The relation between Modulus of elasticity (E), Shear Modulus (G) and Bulk modulus (K) is given by:

\(E = \frac{{9KG}}{{3K + G}}\)

EXPLANATION:

The relation between Modulus of elasticity (E), Shear Modulus (G) and Bulk modulus (K) is given by:

\(E = \frac{{9KG}}{{3K + G}}\)

Now, rewriting the equation as follows:

⇒ 3KE + GE = 9KG

⇒ 3KE – 9KG = - GE

⇒ K(3E – 9G) = - GE

\(\Rightarrow K = \frac{{ - EG}}{{3E - 9G}}\)

\(\Rightarrow K = - \left( {\frac{E}{{\frac{{3E}}{G} - 9}}} \right)\)