Question

If $x=at+b{t}^2$ where $x$ is measured in $m$ and $t$ in $s$, then the dimension of $\left(b/a\right)$ is:

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

Answer 1

Answer: (D)

$\left[T^{-1}\right]$

Given equation is: $x=at+b{t}^2$
The standard equation is: $S=ut+\frac{1}{2}a{t}^2$

$\Rightarrow \left[a\right]=\left[u\right]=L{T}^{-1}$

$\Rightarrow \left[b\right]=\left[a\right]=L{T}^{-2}$

$\Rightarrow \left[\frac{b}{a}\right]=\frac{L{T}^{-2}}{L{T}^{-1}}=\left[T^{-1}\right]$