Some Mechanical Properties of Matter — Physics STD 12 Science — Question

Given:

Bulk modulus of water B = 2.1 × 10⁹Nm^-2

In order to decrease the volume (V) of a water sample by 0.01%, let the increase in pressure be P.

$\frac{\text{v}\times0.1}{100}=\triangle\text{V}$

$\Rightarrow\frac{\triangle\text{V}}{\text{V}}=10^{-4}$

From B $=\frac{\text{P}\text{V}}{\triangle\text{V}},$ We have:

$\Rightarrow\text{P}= \text{B}\Big(\frac{\triangle\text{V}}{\text{V}}\Big)$

$=2.1\times10^{9}\times10^{-4}$

$=2.1\times10^{5}\text{N}/\text{m}^2$

Hence, the requred increase in pressure is 2.1 × 10⁵Nm^-2.