Question

If $v=\frac{a}{t}+b{t}^3$ where, $v=\text{velocity}$ and $t$ is the time. The dimensional formula of $a$ and $b$ respectively are

• A. $\left[T\right],\left[T^{-3}\right]$
• B. $\left[L\right],\left[L{T}^{-4}\right]$
• C. $\left[L^{-1}\right],\left[L{T}^{-3}\right]$
• D. $\left[L^{-1}\right],\left[T^{-3}\right]$

Answer 1

The correct option is B $\left[L\right],\left[L{T}^{-4}\right]$

Given relation is $v=\frac{a}{t}+b{t}^3$
Using principle of dimensional homogeneity
$\Rightarrow \left[v\right]=\left[\frac{a}{t}\right]=\left[b{t}^3\right]$
$\Rightarrow \left[L{T}^{-1}\right]=\left[a{T}^{-1}\right]=\left[b{T}^3\right]$
$\Rightarrow \left[a\right]=\left[L\right]$ and $\left[b\right]=\left[L{T}^{-4}\right]$