Question

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

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

Answer 1

Answer: (B)

$\left[L\right],\left[L{T}^{-4}\right]$

Dimensionally $v=\frac{a}{t}\Rightarrow a=L{T}^{-1}\times T=L$

Also dimensionally $v=b{t}^3\Rightarrow b=\frac{L{T}^{-1}}{T^3}=L{T}^{-4}$