Dimensional formula of modulus of rigidity

Modulus of rigidity

[M L⁻¹ T⁻²]

Written in full: [M¹ L⁻¹ T⁻² A⁰ K⁰]

How to derive it

Modulus of rigidity = Shear stress ÷ Shear strain

Put in the dimensions of each part: [ML⁻¹T⁻²] ÷ [M⁰L⁰T⁰] = [M L⁻¹ T⁻²].

mass (M): 1
length (L): -1
time (T): -2
current (A): 0
temperature (K): 0

SI unit

The SI unit of modulus of rigidity is pascal (Pa).

Same dimensions as modulus of rigidity

These quantities have exactly the same dimensions, a favourite trick in JEE and NEET "which pair has the same dimensions" questions:

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More from Elasticity

Quantity	Formula
Compressibility	[M⁻¹ L T²]
Strain	[M⁰ L⁰ T⁰]
Poisson's ratio	[M⁰ L⁰ T⁰]