Question

what is moulds of rigidity and derive the expression of it​

Answer 1

Explanation:

shears stress is the ratio of tension per unit area while shears strain is the ratio of change in length to unit original length. so, modulus of rigidity or shears modulus, it is the expression for the Modulus of rigidity. now, S.I unit of is N/m² or Pascal.

Answer 2

Answer:

Shear modulus also known as Modulus of rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ.

Shear Modulus of elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young’s modulus and bulk modulus. The shear modulus of material gives us the ratio of shear stress to shear strain in a body.

Measured using the SI unit pascal or Pa.

The dimensional formula of Shear modulus is M1L-1T-2.

It is denoted by G.

It can be used to explain how a material resists transverse deformations but this is practical for small deformations only, following which they are able to return to the original state. This is because large shearing forces lead to permanent deformations (no longer elastic body).

Formula :

$G=\frac{\tau _{xy}}{\gamma _{xy}}=\frac{\left ( \frac{F}{A} \right )}{\left ( \frac{\Delta x}{l} \right )}=\frac{Fl}{A\Delta x}$

Where,

$\tau _{xy}=\frac{F}{A} \: is \: shear \: stress.$

F is the force acting on the object.

A is the area on which the force is acting.

$\gamma _{xy}=\frac{\Delta x}{l} \: \: is \: the \: shear \: strain.$

Δx is the transverse displacement.

l is the initial length