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].
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