Question

If force, velocity and time are taken as fundamental quantities, find the dimensions of work.

• A. $\left[F^{0}V{T}^{-1}\right]$
• B. $\left[FV{T}^2\right]$
• C. $\left[F{V}^2{T}^{-1}\right]$
• D. $\left[FVT\right]$

Answer 1

The correct option is D $\left[FVT\right]$

As the work done is given by
$W=$force$\times$displacement
Dimension of force $F=\left[M^1{L}^1{T}^{-2}\right]$,
Displacement $x=\left[L^1\right]$
So the dimension of work done $\left[W\right]=M{L}^2{T}^{-2}$
According to question
$\left[W\right]=\left[F{]}^a\right[V{]}^b{T}^c$
Substituting the values of dimensions, we get $M{L}^2{T}^{-2}=\left[M{L}^2{T}^{-2}{]}^a\right[L{T}^{-1}{]}^b{T}^c$
Comparing the powers, we get
$a=1,a+b=2\Rightarrow b=1\text{and}c-2a-b=-2\Rightarrow c=1$
So, $\left[W\right]=\left[FVT\right]$
Final Answer: (a)