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].

⇒ Check Other Dimensional Formulas:

• Dimensions of Impedance
• Dimensions of Weight
• Dimensions of Linear Density
• Dimensions of Gravitational Potential Energy
• Dimensions of Pressure

Hooke’s Law