Dimensions of Coefficient of Elasticity

Dimensional Formula of Coefficient of Elasticity

The dimensional formula coefficient of elasticity is given by,

[M1 L-1 T-2]

Where,

  • M = Mass
  • L = Length
  • T = Time

Derivation

Coefficient of Elasticity = Stress × [Strain]-1 . . . . (1)

Since, Stress = Force × [Area]-1 . . . (2)

And, Force = M × a = [M × LT-1 × T-1]

∴ The dimensions of force = [M1 L1 T-2] . . . . (3)

The dimensional formula of area = [M0 L2 T0] . . . . (4)

On substituting equation (3) and (4) in equation (2) we get,

Stress = Force × [Area]-1 = [M1 L1 T-2] × [M0 L2 T0]-1

Therefore, the dimensional formula of stress = [M1 L-1 T-2] . . . . (5)

And, Strain = ΔL × L-1

∴ the dimensions of Strain = [M0 L0 T0] . . . . (6)

On substituting equation (5) and (6) in equation (1) we get,

Coefficient of Elasticity = Stress × [Strain]-1

Or, Elasticity = [M1 L-1 T-2] × [M0 L0 T0]-1 = [M1 L-1 T-2].

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

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