What is compressibility? Give its unit and dimensional formula.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) Compressibility is defined as the reciprocal of the bulk modulus $(B)$. It represents the fractional change in volume per unit increase in pressure.
The formula for compressibility $(k)$ is:
$k = \frac{1}{B} = -\frac{1}{V} \left( \frac{\Delta V}{\Delta p} \right)$
Unit:
The $SI$ unit of compressibility is $Pa^{-1}$ or $m^2/N$.
Dimensional Formula:
Since $B = \frac{\text{Force}}{\text{Area}} \times \frac{\text{Volume}}{\text{Change in Volume}}$,the dimensions of $B$ are $[M L^{-1} T^{-2}]$.
Therefore,the dimensional formula for compressibility is $[M^{-1} L^1 T^2]$.

Explore More

Similar Questions

The compressibility of water is $6 \times 10^{-10} \ N^{-1} \ m^2$. If one litre is subjected to a pressure of $4 \times 10^7 \ N \ m^{-2}$,the decrease in its volume is (in $cc$):

The compressibility of a material is defined as:

$A$ solid copper cube of $7 \,cm$ edge is subjected to a hydraulic pressure of $8000 \,kPa$. The volume contraction of the copper cube is (Bulk modulus of copper $= 140 \,GPa$)

The increase in pressure required to decrease the $200\,L$ volume of a liquid by $0.004\%$ in a container is ............ $kPa$. (Bulk modulus of the liquid $= 2100\,MPa$)

Difficult
View Solution

Compute the fractional change in volume of a glass slab,when subjected to a hydraulic pressure of $10 \; atm$.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo