Question

the young s modules of steel is 2×10^11N/m^2 and rigidity modules is 8×10^10N/m^2 find tune poisson ratio and bulk modules​

Answer 1

Answer:

Poisson's ratio is 0.25 and bulk modulus is 1.33×10¹¹ N/m².

Explanation:

Given :-

• The Youngs modulus of steel is 2×10¹¹ N/m².
• Rigidity modulus is $\sf{8\times\:10^{10}}$ N/m².

To find :-

• Poisson's ratio and bulk modulus.

Solution :-

Formula used :

${\boxed{\sf{Y=2n(1+\sigma)}}}$

• Terms identification :-
• Y = Young's modulus
• n = Rigidity modulus
• $\sf{\sigma}$=Poisson's ratio

$\sf{Y=2n(1+\sigma)}$

$\to\sf{2\times\:10^{11}=2\times\:8\times\:10^{10}(1+\sigma)}$

$\to\sf{1+\sigma=\dfrac{2\times\:10^{11}}{2\times\:8\times\:10^{10}}}$

$\to\sf{1+\sigma=1.25}$

$\to\sf{\sigma=1.25-1}$

$\to\sf{\sigma=0.25}$

Therefore, poisson's ratio is 0.25.

Formula used :-

${\boxed{\sf{Y=3K(1-2\sigma)}}}$

• Terms identification :-
• Y = Young's modulus
• K = Bulk modulus
• $\sf{\sigma}$=Poisson's ratio

$\sf{Y=3K(1-2\sigma)}$

$\to\sf{2\times\:10^{11}=3K(1-2\times\:0.25)}$

$\to\sf{2\times\:10^{11}=3K\times\:0.5}$

$\to\sf{K=\dfrac{2\times\:10^{11}}{0.5\times\:3}}$

$\to\sf{K=1.33\times\:10^{11}}$

Therefore, the bulk modulus is 1.33 × 10¹¹ N/m².

Answer 2

Poisson's ratio is 0.25 and bulk modulus is 1.33×10¹¹ N/m².

$\boxed{Given :-}$

The Youngs modulus of steel is 2×10¹¹ N/m².

Rigidity modulus is $\sf{8\times\:10^{10}}$

$\boxed{To find :-}$

Poisson's ratio and bulk modulus.

$\boxed{Solution :-}$

Formula used :

Y=2n(1+σ)

here,

Y = Young's modulus

n = Rigidity modulus

σ =Poisson's ratio

Y=2n(1+σ)

$\to\sf{2\times\:10^{11}=2\times\:8\times\:10^{10}(1+\sigma)}$

$\to\sf{1+\sigma=\dfrac{2\times\:10^{11}}{2\times\:8\times\:10^{10}}}$

→1+σ=1.25

→σ=1.25−1

→σ=0.25

Therefore, poisson's ratio is 0.25.

here,

Y = Young's modulus

K = Bulk modulus

$\sf{\sigma}σ$ =Poisson's ratio

$\sf{Y=3K(1-2\sigma)}$

$\to\sf{2\times\:10^{11}=3K(1-2\times\:0.25)}$

$\to\sf{2\times\:10^{11}=3K\times\:0.5}$

-> 1.33 × 10¹¹

the bulk modulus is 1.33 × 10¹¹ N/m².