Dimensional Formula of Bulk Modulus

The dimensional formula of bulk modulus is given by,

[M¹ L^-1 T^-2]

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Bulk modulus (k) = Bulk Stress × [Bulk strain]^-1 . . . . (1)

Since Bulk stress = Force × [Area]^-1 . . . (2)

The dimensional formula of,

Force = [M¹ L¹ T^-2] . . . . (3)

Area = [M⁰ L² T⁰] . . . . (4)

On substituting equation (3) and (4) in equation (2) we get,

Bulk stress = [M¹ L¹ T^-2] × [M⁰ L² T⁰]^-1

Therefore, the dimensions of Bulk stress = [M¹ L^-1 T^-2] . . . . . (5)

And, Bulk strain = Change in Volume × Volume^-1

= ΔV/V = [M⁰ L⁰ T⁰] = Dimensionless Quantity . . . (6)

On substituting equation (5) and (6) in equation (1) we get,

Bulk modulus = Bulk Stress × [Bulk strain]^-1

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

Therefore, the bulk modulus is dimensionally represented as [M¹ L^-1 T^-2].

⇒ Check Other Dimensional Formulas:

• Dimensions of Joule
• Dimensions of Reynolds Number
• Dimensions of Permittivity
• Dimensions of Linear Density
• Dimensions of Gravitational Potential Energy

Hooke’s Law