Dimensional Formula of Modulus of Elasticity
The dimensional formula of modulus of elasticity is given by,
[M1 L-1 T-2]
Where,
- M = Mass
- L = Length
- T = Time
Derivation
Modulus of Elasticity = Linear Stress × [Linear Strain]-1 . . . . . . (1)
The dimensional formula of length = [M0 L1 T0] . . . . . (2)
Since, stress = Force × [Area]-1 . . . . . (3)
⇒ The dimensions of,
- Force = m × a = [M1 L1 T-2] . . . . (4)
- Area = Length × Breadth = [M0 L2 T0] . . . . (5)
On substituting equation (4) and (5) in equation (3) we get,
Stress = [M1 L1 T-2] × [M0 L2 T0]-1
Therefore, the doimensional formula of linear stress = [M1 L-1 T-2] . . . (6)
And, the dimensional formula of linear strain = [M0 L0 T0] . . . (7)
On substituting equation (6)and (7) in equation (1) we get,
Modulus of Elasticity = Linear Stress × [Linear Strain]-1
Or, E = [M1 L-1 T-2] × [M0 L0 T0]-1 = [M1 L-1 T-2]
Therefore, the modulus of elasticity is dimensionally represented as [M1 L-1 T-2].
Comments