Question

The SI unit of a physical is $\left[ {{J}_{m}}^{-2} \right]$. The dimensional formula for that quantity is:
(A) ${{M}^{1}}{{L}^{-2}}$
(B) ${{M}^{1}}{{L}^{0}}{{T}^{-2}}$
(C) ${{M}^{1}}{{L}^{2}}{{T}^{-1}}$
(D) ${{M}^{1}}{{L}^{-1}}{{T}^{-2}}$

Answer 1

Hint: We should know that the SI system, also called the metric system, is used around the world. There are seven basic units in the SI system: the meter (m), the kilogram (kg), the second (s), the kelvin (K), the ampere (A), the mole (mol), and the candela (cd). The prefixes used in SI are from Latin and Greek, and they refer to the numbers that the terms represent. SI is used in most places around the world, so our use of it allows scientists from disparate regions to use a single standard in communicating scientific data without vocabulary confusion.

Complete step-by step answer:
We should know that the equations obtained when we equal a physical quantity with its dimensional formulae are called Dimensional Equations. The dimensional equation helps in expressing physical quantities in terms of the base or fundamental quantities.
So, we can say that dimension formula tells about which fundamental quantities are there in the physical quantity given. It is represented in square brackets.
$\left[ {{J}_{m}}^{-2} \right]=\left[ \dfrac{{{M}^{1}}{{L}^{2}}{{T}^{-2}}}{{{L}^{2}}} \right]=\left[ {{M}^{1}}{{L}^{0}}{{T}^{-2}} \right]$

Hence, the correct answer is Option B.

Note: It should be known to us that dimensional analysis is used for three prominent reasons:
(1) To check the consistency of a dimensional equation.
(2) To derive the relation between physical quantities in physical phenomena.
(3) To change units from one system to another.
We should however know the limitations of dimensional equation as:
Dimensional Analysis can't derive relation or formula if a physical quantity depends upon more than three factors having dimensions. It can't derive a formula containing trigonometric function, exponential function, and logarithmic function and it can't derive a relation having more than one part in an equation.