Question

If force $F$, work $W$ and velocity $v$ are taken as fundamental quantities. What is the dimensional formula of time?

Answer 1

Fundamental Quantity: It is an independent physical quantity that is used to define other physical quantities.

Dimensional formula: It is an expression that shows the power to which a fundamental quantity is used to obtain one unit of a derived quantity.

Step 1: Given

Force$=F$

Work$=W$

Velocity$=v$

Step 2: Determining the dimensional formula of time

Let the distance be $d$ and the time be $t$

Distance can be expressed as, $d=v\times t$

Work done by an object is given by,

$$\begin{gathered} W=F\times d \\ =F\times v\times t \\ t=\frac{W}{Fv} \\ t=[W{F}^{-1}{v}^{-1}] \end{gathered}$$

Hence, the dimensional formula of the time will be $[W{F}^{-1}{v}^{-1}]$.