Question

Find the SI unit of a physical quantity of the dimensional formula of the quantity is $[{M^1}{L^1}{T^{-2}}]$
(A) $kg {s^{-2}}{m^{-1}}$
(B) $kg m{s^{-2}}$
(C) ${kg^2}{s^2}{m^2}$
(D) $kg m{s^2}$

Answer 1

Hint
The SI system consists of seven base units which are then used to denote the dimensional formula of a physical quantity. The SI unit of a physical quantity can be derived by denoting the units for given dimensional units.

Complete step by step answer
Given, the dimensional formula of the physical quantity is $\left[ {{{\rm{M}}^1}{{\rm{L}}^1}{{\rm{T}}^{ - 2}}} \right]$.
The units of given dimension are represented by,

Base Quantity	Base Unit	Symbol	Dimensions
Length	Meter	m	[L]
Mass	Kilogram	kg	[M]
Time	Second	s	[T]

On considering the above table,
$\left[ {{{\rm{M}}^1}{{\rm{L}}^1}{{\rm{T}}^{ - 2}}} \right] = \dfrac{{{\rm{Mass}} \times {\rm{Length}}}}{{{\rm{Secon}}{{\rm{d}}^2}}} = {\rm{kgm}}{{\rm{s}}^{ - 2}}$
Therefore, (B) ${\rm{kgm}}{{\rm{s}}^{ - 2}}$ is the required solution.

Additional Information
The dimensions are used to describe the nature of the physical quantities. All the derived units can be obtained from the combination of base units; similarly, their dimensions can also be derived from dimensions of base units. The seven base units are length (meter), mass (kilogram), time (second), electric current (Ampere), thermodynamic temperature (Kelvin), amount of substance (mole), and luminous intensity (Candela).

Note
The power of dimensional formula should be considered accurate because it may change the unit of the physical quantity. The dimensional formula $\left[ {{{\rm{M}}^1}{{\rm{L}}^1}{{\rm{T}}^{ - 2}}} \right]$ represents the physical quantity ‘Force’ whose SI unit is ‘${\rm{kgm}}{{\rm{s}}^{ - 2}}$’ or ‘Newton’ denoted by ‘N’. There are different types of force such as magnetic force, electric force, gravitational force and others, we study in physics but all have same unit ‘Newton’ or ‘${\rm{kgm}}{{\rm{s}}^{ - 2}}$’.