Dimensions of Bulk Modulus

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].

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