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# The S.I. unit of compressibility is?A. $\dfrac{{{m^2}}}{N}$ B. $N{m^2}$C. $\dfrac{N}{{{m^2}}}$D. $\dfrac{{kg}}{{{m^3}}}$

Last updated date: 29th Feb 2024
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Hint:Let us understand the unit first. A unit of measurement is a definite magnitude of a quantity that is used as a norm for measuring the same kind of quantity. It is described and accepted by convention or by law.

The compressibility $\kappa$(denoted $\beta$in some fields) can be expressed in its simplest form as
$\kappa = - \dfrac{1}{V}\dfrac{{\partial V}}{{\partial p}}$
where $V$ stands for volume and $p$ stands for pressure. In the (usual) case where a rise in pressure causes a reduction in volume, the option to describe compressibility as the negative of the fraction renders compressibility positive. The isothermal bulk modulus is the inverse of compressibility at a fixed temperature.
When we discuss compressibility, we usually refer to it as the opposite or reciprocal of the bulk modulus of elasticity. So, when we talk about compressibility units, we're talking about mutual pressure units. The SI unit of compressibility is given as $\dfrac{{{m^2}}}{N}$.