Question

A system of units uses force $\left(F\right)$, acceleration $\left(A\right)$ and time $\left(T\right)$ as their fundamental physical quantities. The dimension of length in the system is

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

Answer 1

The correct option is D $\left[A{T}^2\right]$

We know that acceleration is defined as the rate of change of velocity.
$\Rightarrow a=\frac{\Delta v}{\Delta t}$
$\Rightarrow \left[a\right]=\frac{\left[\Delta v\right]}{\left[\Delta t\right]}$
$\Rightarrow \left[A\right]=\frac{\left[L{T}^{-1}\right]}{\left[T\right]}$
$\Rightarrow \left[A\right]=\left[L{T}^{-2}\right]$
$\Rightarrow \left[L\right]=\left[A{T}^2\right]$