Question

M
OHA
** *** ** *** **
Out of the following, Identify the correct relation between Young's modulus,
Bulk modulus and Modulus of rigidity
1) 1/Y = 1/3n + 1/9K 2 ) 1/3Y = 1/n +1/9K
3) 1/9Y = 1/34 + 1/K 4) 1/Y = 3/n + 9/
K
T​

Answer 1

Given, Y is Young's modulus, K is bulk modulus and η is modulus of rigidity ( it is also known as shear modulus).

we have to find the relation between Young's modulus, Bulk modulus and modulus of rigidity.

relation between Young's modulus and modulus of rigidity

Y = 2η(1 + μ) ......(1), where μ is poisson's ratio.

relation between Young's modulus and bulk modulus

Y = 3K(1 - 2μ) ........(2)

from equations (1) and (2) after eliminating μ we get, Y/2η - 1 = (1 - Y/3K)/2

⇒(Y - 2η)/η = 1 - Y/3K

⇒Y/η - 2 = 1 - Y/3K

⇒Y/η + Y/3K = 3

⇒1/η + 1/3K = 3/Y

⇒1/3η + 1/9K = 1/Y

therefore, option (1) is correct choice.