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].

⇒ Check Other Dimensional Formulas:

• Dimensions of Newton
• Dimensions of Boltzmann Constant
• Dimensions of Time Period
• Dimensions of Power of Lens
• Dimensions of Gravitational Potential Energy