Question

Dimensions of frequency are :
A. $[{{M}^{0}}{{L}^{-1}}{{T}^{0}}]$
B. $[{{M}^{0}}{{L}^{0}}{{T}^{-1}}]$
C. $[{{M}^{0}}{{L}^{0}}{{T}^{{}}}]$
D. $[M{{T}^{-2}}]$

Answer 1

We are supposed to find the dimensional formula of frequency. For that, we have to analyse the definition and the numerical formula of the same. Further, we can deduce the dimensional formula by finding the degree of dependence of a physical quantity on another. The principle of consistency of two expressions can be used to find the equation relating these two quantities.
We know that frequency is the number of oscillations that occur in one second. In other words, frequency is the reciprocal of time period.

Formulas used:
$f=\dfrac{1}{T}$, where $f$ is the frequency and $T$is the time period.

Complete step by step answer:
We know that the value of frequency is obtained by taking the reciprocal of the time period.
i.e. $f=\dfrac{1}{T}$
The SI unit of time period is ‘second’ (s)
Hence, $f=\dfrac{1}{T}$
$\begin{aligned} & \therefore \dfrac{1}{s}={{s}^{-1}} \\\ \end{aligned}$
The dimensional formula for time is $[T]$
Hence its inverse is represented as $[{{T}^{-1}}]$
Therefore, we can represent the dimensional formula of frequency as $[{{M}^{0}}{{L}^{0}}{{T}^{-1}}]$
Therefore, option B is the correct choice among the four.

Note: Dimensional formula is widely used in many areas. However, there are a few problems along the way. Dimensionless quantities and proportionality constant cannot be determined in this way. It does not apply to trigonometric, logarithmic and exponential functions. When we look at a quantity that is dependent on more than three quantities, this approach will be difficult. In line with all of this, if one side of our equation has addition or subtraction of quantities, this approach is not appropriate.