Question

The pressure of a medium is changed from $1.01\times {10}^{5}Pa$ to $1.165\times {10}^{5}Pa$ and change in volume is $10\%$ keeping temperature constant. The bulk modulus of the medium is

• A. $1.55\times {10}^{5}Pa$
• B. $107.04\times {10}^{5}Pa$
• C. $205\times {10}^{5}Pa$
• D. $53.07\times {10}^{5}Pa$

Answer 1

The correct option is A $1.55\times {10}^{5}Pa$

Given, pressure change from $1.01\times {10}^{5}Pa$ to $1.165\times {10}^{5}Pa$
Change in pressure,
$p=(1.165-1.01)\times {10}^5$
Change in volume, $\Delta V=10\%$
As we know, the bulk modulus of any object is given by
$K=\frac{\text{normal stress}}{\text{Volumetric strain}}$
$K=\frac{\frac{F}{A}}{\frac{\Delta V}{V}}=\frac{-pV}{\Delta V}$
$K=\frac{VP}{\Delta V}=\frac{(1.165-1.01\times {10}^5)}{\left(10/100\right)Pa}$
$K=1.55\times {10}^{5}Pa$