Question

A spherical ball contracts by 0.001% when it is subjected to a pressure of 100 atm. Calculate its bulk modulus.

Answer 1

Hint:We know that when materials are subjected to some force then it may contract or expand. For example, if a force is applied on a wire then it may extend in its length. There can be change in length, change in the area or change in the volume. When we talk about the change in the volume, we can talk in terms of bulk modulus.

Complete step by step answer:
Bulk modulus is defined as the ratio of the volumetric stress to the volumetric strain and it is unique for every material. Since it is a ratio of stress and strain, we know the SI unit of stress is $N/{{m}^{2}}$ or $Pa$ and strain is a unitless quantity. So, the SI unit is the same pascals denoted as $Pa$.
Now given data is the question,
$\dfrac{\Delta V}{V}=0.001%$
$\Rightarrow \dfrac{\Delta V}{V}=0.001\times \dfrac{1}{100}$
$\Rightarrow \dfrac{\Delta V}{V}={{10}^{-5}}$
Normal stress is given to be $100atm$, we know $1atm={{10}^{5}}Pa$
$\Rightarrow 100\times {{10}^{5}}={{10}^{7}}Pa$
Therefore, Bulk modulus can be given as,
$\therefore \dfrac{{{10}^{7}}}{{{10}^{-5}}}={{10}^{12}}$Pa

So, the Bulk Modulus comes out to be ${{10}^{12}}Pa$.

Note: Bulk modulus in simple words can be defined as the property of a material or a substance when it is subjected to pressure. Bulk modulus is denoted by the symbol $K$. Greater be the value of bulk modulus, the higher is its nature to be incompressible. The concept of Bulk Modulus is also used in liquids. Temperatures of fluid and entrained air content are the two factors highly controlled by the bulk modulus.