Question

The S.I. unit of compressibility is:

• A. N/m\(^2\)
• B. N/m\(^2\)s
• C. m\(^2\)/N
• D. Ns/m\(^2\)

Hint:

Remembering that compressibility is the inverse of stiffness (bulk modulus) is key. Stiff materials have a high bulk modulus and low compressibility, while easily compressed materials have a low bulk modulus and high compressibility.

Answer 1

The Correct Option is C

Step 1: Define compressibility. Compressibility (\(\kappa\)) is a measure of the relative volume change of a fluid or solid as a response to a pressure change. It is defined as the reciprocal of the bulk modulus (\(B\)). \[ \kappa = \frac{1}{B} \]
Step 2: Determine the S.I. unit of bulk modulus. Bulk modulus is defined as the ratio of pressure stress to volumetric strain: \[ B = -\frac{\Delta P}{\Delta V / V_0} \] Since volumetric strain (\(\Delta V / V_0\)) is dimensionless, the unit of bulk modulus is the same as the unit of pressure. The S.I. unit of pressure is the Pascal (Pa), which is equivalent to Newtons per square meter (N/m\(^2\)).
Step 3: Determine the S.I. unit of compressibility. Since compressibility is the reciprocal of bulk modulus, its unit is the reciprocal of the unit of pressure. \[ \text{Unit of } \kappa = \frac{1}{\text{Unit of } B} = \frac{1}{\text{N/m}^2} = \frac{\text{m}^2}{\text{N}} \]