Question

Dimension of Pressure are same as that of
(A) Energy
(B) Energy per unit Volume
(C) Force
(D) Force per unit Volume

Answer 1

Hint: In order to solve this question, we should know that every physical quantity can be expressed in terms of its dimensions using seven fundamental physical quantities. Here, we will derive the dimensional formula of pressure and will match it with the given options.

Complete Step by Step Solution:
As we know that, mathematically pressure is defined as the force per unit area acting on a body and it can be written as $P = \dfrac{F}{A}$ here, F is the force which have dimensional formula of $[F] = [ML{T^{ - 2}}]$ and A represent area having dimensional formula of $[A] = [{L^2}]$ now using these values we get the dimensional formula of pressure as
$ [P] = \dfrac{{[ML{T^{ - 2}}]}}{{[{L^2}]}} \\$
$ [P] = [M{L^{ - 1}}{T^{ - 2}}] \\ $

So, Dimensional Formula of Pressure is $[P] = [M{L^{ - 1}}{T^{ - 2}}]$ now, Let us derive the dimensional formula for given option (B) Energy per unit volume.

Since the dimensional formula of Energy is given as $[M{L^2}{T^{ - 2}}]$ and energy per unit volume is the ratio of energy and volume, so dimensions of volume is $[{L^3}]$ using this we get the dimensions of energy per unit volume as $[M{L^{ - 1}}{T^{ - 2}}]$ so, we see that Dimensional formula of pressure is same as that of Energy per unit volume which is $[M{L^{ - 1}}{T^{ - 2}}]$

Hence, the correct option is (B) Energy per unit Volume.

Note: It should be remembered that there are only seven fundamental physical quantities whose dimensions can be used to determine any other physical quantity dimensions and these seven fundamental quantities are Mass, Length, Time, Current, Luminous Intensity, Temperature, and Amount of Substance.