# Dimensions of Modulus of Elasticity

## 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 LT0] . . . . . (2)

Since, stress = Force × [Area]-1 . . . . . (3)

⇒ The dimensions of,

• Force = m × a = [M1 LT-2] . . . . (4)
• Area = Length × Breadth = [M0 LT0] . . . . (5)

On substituting equation (4) and (5) in equation (3) we get,

Stress = [M1 LT-2] × [M0 LT0]-1

Therefore, the doimensional formula of linear stress = [M1 L-1 T-2] . . . (6)

And, the dimensional formula of linear strain = [M0 LT0] . . . (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 LT0]-1 = [M1 L-1 T-2]

Therefore, the modulus of elasticity is dimensionally represented as [M1 L-1 T-2].