Dimensional Formula of Modulus of Rigidity

The dimensional formula of modulus of rigidity is given by,

[M¹ L^-1 T^-2]

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Modulus of Rigidity (μ) = shear stress × [shear strain]^-1 . . . . (1)

Since, strain = ΔL/L = Dimensionless Quantity . . . . (2)

And, Stress = Force × [Area]^-1 . . . . . (3)

The dimensional formula of,

Area = [M⁰ L² T⁰] . . . . (4)

Force = [M¹ L¹ T^-2] . . . . . (5)

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

Stress = [M¹ L¹ T^-2] × [M⁰ L² T⁰]^-1

∴ The dimensions of stress = [M¹ L^-1 T^-2] . . . . (6)

On substituting equation (2) and (6) in equation (1) we get,

Modulus of Rigidity (μ) = shear stress × [shear strain]^-1

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

Therefore, the Universal Gravitational Constant is dimensionally represented as [M¹ L^-1 T^-2].

⇒ Check Other Dimensional Formulas:

• Dimensions of Time Period
• Dimensions of Momentum
• Dimensions of Linear Density
• Dimensions of Gravitational Potential Energy
• Dimensions of Dipole Moment