Question

what will be modulus of rigidity if the value of modulus of elasticity is 200 and Poissons ratio is 0.25

a) 70
b) 80
c) 125
d) 250​

Answer 1

Option b is correct.

• The shear One indicator of a solid's mechanical qualities is its modulus of elasticity. Young's modulus and bulk modulus are additional elastic moduli. We can determine the body's ratio of shear stress to shear strain by looking at a material's shear modulus.
• It can be applied to describe how a material resists transverse deformations, however this is only useful for tiny deformations before they can return to their original shape. This is due to the fact that strong shearing pressures induce lasting deformations (no longer elastic body). When lateral deformation is caused by the application of a shear force, the elastic coefficient is the modulus of rigidity. It allows us to quantify how stiff a body is.

Here, according to the given information, we are given that, modulus of elasticity is 200 and Poisson's ratio is 0.25.

Now, we know that,

$E = G(1+$Poisson's ratio$)$

Then, $G = \frac{200}{2(1+0.25)} =80.$

Hence, option b is correct.

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Answer 2

The correct option about the modulus of rigidity of material having the value of modulus of elasticity is 200 and Poisson's ratio is 0.25 is b) 80 N/m².

Given:

The value of the modulus of elasticity is 200 and the Poissons ratio is 0.25.

To Find:

The modulus of rigidity.

Solution:

Modulus of rigidity is the property of solids which is the measure of stiffness and is calculated by the ratio of stress and strain.

Modulus of elasticity is the property of a substance by which it resists the deforming force to be deformed elastically.

Poisons ratio is the ratio of two scalar quantities width and length.

To find the modulus of rigidity we will follow the following steps:

As we know,

The relation between the modulus of rigidity, modulus of elasticity, and Poisson's ratio are:

E = 2G ( 1 + u )

Here,

E = modulus of elasticity

G = modulus of rigidity

u = Poisson's ratio

Now,

Putting values in the above formula we get,

200 = 2 × G ( 1 + 0.25 )

200 = 2G + 0.5G

200 = 2.5 G

G =

$\frac{200}{2.5} = 80 N/m²$

Henceforth, the correct option about the modulus of rigidity of material having the value of modulus of elasticity is 200 and Poissons ratio is 0.25 is b) 80 N/m².

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