Question

what is the dimension formula of modulus of rigidity?

Answer 1

what is the dimension formula of modulus of rigidity?

Answer:

In materials science, shear modulus or **modulus of rigidity**, denoted by $G$, or sometimes $S$ or $\mu$, is defined as the ratio of shear stress to the shear strain:

$$G = \frac{\tau_{xy}}{\gamma_{xy}} = \frac{F / A}{\Delta x / l} = \frac{Fl}{A \Delta x}$$

where

$\tau_{xy} = \frac{F}{A} =$ shear stress;

$F$ is the force which acts,

$A$ is the area on which the force acts

$\gamma_{xy} = \frac{\Delta x}{l} = \tan \Theta =$ shear strain.

$\Delta x$ is the transverse displacement

$l$ is the initial length

In SI $\Delta x$ and $l$ are in units of length $[L]$

Force $F$ is measured in Newton = $[MLT^{-2}]$

Area in in units of square length $[L^2]$

Thus, formula for modulus of rigidity become:

$$G = \frac{Fl}{A \Delta x} = \frac{[MLT^{-2}] [L]}{[L^2] [L]} = [ML^{-1}T^{-2}]$$

Answer: $[ML^{-1}T^{-2}]$