What is the dimensional formula for compressibility?

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Detailed Solution

The dimensional formula for compressibility is [M⁻¹ L¹ T²].

Compressibility tells how much a substance can be compressed when pressure is applied. It is the reciprocal of bulk modulus (B).

Compressibility (K) = 1 / Bulk Modulus (B)

Bulk modulus = Pressure / (Change in volume ÷ Original volume)
Pressure = Force / Area = (Mass × Acceleration) / Area = [M L T⁻²] / [L²] = [M L⁻¹ T⁻²]
So, bulk modulus B has dimensions of [M L⁻¹ T⁻²]
Compressibility = 1 / B = [M⁻¹ L¹ T²]

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