Question

Bulk modulus of water is \[2\times {{10}^{9}}N/{{m}^{2}}\]. The change in pressure required to increase the density of water by \[0.1\%\]is
A. \[2\times {{10}^{9}}N/{{m}^{2}}\]
B. \[2\times {{10}^{8}}N/{{m}^{2}}\]
C. \[2\times 10{}^{6}N/{{m}^{2}}\]
D. \[2\times {{10}^{4}}N/{{m}^{2}}\]

Answer 1

Hint: Bulk implies healthy, it could be said it alludes to the entire of the material, for example Volume. Basically, any modulus is the proportion between worry to strain. Any Modulus is a proportion of the protection from distortion.

Complete answer:
The correct answer is C.
\[K=\dfrac{\Delta P}{\Delta V/V}\]
\[\Delta P=K\dfrac{\Delta V}{V}=2\times {{10}^{9}}\times \dfrac{0.1}{100}=2\times {{10}^{6}}N/{{m}^{2}}\]
Bulk modulus is defined as the proportion of the volumetric stress related to the volumetric strain for any material. In the very simpler words, the bulk modulus is nothing but a numerical constant that is used to measure and describe the elastic properties of any solid or a liquid when pressure is applied.
Bulk modulus is a modulus associated with a volume strain when a volume is compressed. The formula for bulk modulus is:
\[bulk\text{ }modulus\text{ }=-\dfrac{\text{ }pressure\text{ }applied\text{ }}{fractional\text{ }change\text{ }in\text{ }volume}\]
So as with all moduli, we'll define the bulk modulus as the pressure that we applied divided by the fractional change in volume.
Sometimes the bulk modulus is referred to as the incompressibility. The bulk modulus is a measure of the ability of a substance to withstand changes in volume when under compression on all sides. It is equal to the quotient of the applied pressure divided by the relative deformation.

Note: Most of the times young's modulus, and the bulk modulus, are termed to be similar, but the basic difference between young's modulus, and the bulk modulus, is that Young's modulus is the ratio of the present tensile stress to tensile strain, the bulk modulus is the ratio of volumetric stress to volumetric strain and shear modulus is the ratio of shear stress to shear strain.