Question

Which of the options given will be the dimension of the Bulk Modulus?
$\begin{align}
  & A.M{{L}^{-1}}{{T}^{-1}} \\
 & B.M{{L}^{-1}}{{T}^{-2}} \\
 & C.ML{{T}^{2}} \\
 & D.ML{{T}^{-1}} \\
\end{align}$

Answer 1

Hint: The bulk modulus of a material is defined as the amount of how this material opposes compression occurring for it. It can be sometimes shown as the ratio of the infinitesimal increase in pressure to the net relative decrease in the volume.
The strain is not having any units and therefore the bulk's modulus will be having the units of pressure. This will help you in solving this question.

Complete step by step answer:
 The bulk modulus of a material is defined as the amount of how this material opposes compression occurring for it. It can be sometimes shown as the ratio of the infinitesimal increase in pressure to the net relative decrease in the volume. As the bulk modulus is defined as ratio of the pressure to the volumetric strain, we can write it as an equation,
$B=\dfrac{F}{A}$
Therefore the dimension of the ratio will be given as,
$\begin{align}
  & B=\dfrac{ML{{T}^{-2}}}{{{L}^{2}}} \\
 & B=M{{L}^{-1}}{{T}^{-2}} \\
\end{align}$
Thus this is the dimension of bulk modulus.
The strain is not having any units and therefore the bulk's modulus will be having the units of pressure.

So, the correct answer is “Option B”.

Note: Other modulus were describing the response of the material which is basically strain to other types of stress. The shear modulus of a material defines the response to shear, and the young’s modulus explains the response to linear stress. In the case of fluid, the bulk modulus of a material is the only thing acting. In the case of complex anisotropic solid like paper or wood, these three moduli do not include enough data to explain its nature.