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 (\(\kappa\)) quantifies the relative change in volume of a substance due to a pressure change. It is mathematically expressed as the inverse of the bulk modulus (\(B\)). \[ \kappa = \frac{1}{B} \]
Step 2: Determine the S.I. unit of bulk modulus. Bulk modulus (\(B\)) is calculated as the ratio of pressure stress to volumetric strain: \[ B = -\frac{\Delta P}{\Delta V / V_0} \] Given that volumetric strain (\(\Delta V / V_0\)) is dimensionless, the unit of bulk modulus mirrors that of pressure. The S.I. unit for pressure is the Pascal (Pa), equivalent to Newtons per square meter (N/m\(^2\)).
Step 3: Determine the S.I. unit of compressibility. As compressibility is the reciprocal of bulk modulus, its unit is the inverse of the bulk modulus unit. \[ \text{Unit of } \kappa = \frac{1}{\text{Unit of } B} = \frac{1}{\text{N/m}^2} = \frac{\text{m}^2}{\text{N}} \]