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

If $v=\frac{a}{t}+b t^{3}$ where $v=$ velocity and $t$ is time The dimensional formula of a and b are
  1. $[\mathrm{T}],\left[\mathrm{T}^{-3}\right]$
  2. $[\mathrm{L}],\left[\mathrm{LT}^{-4}\right]$
  3. $\left[\mathrm{T}^{-3}\right],[\mathrm{T}]$
  4. $\left[\mathrm{LT}^{-4}\right],[\mathrm{L}]$

Solution

Dimensionally $\mathrm{v}=\frac{\mathrm{a}}{\mathrm{t}} \Rightarrow \mathrm{a}=\mathrm{LT}^{-1} \times \mathrm{T}=\mathrm{L}$
also dimensionally $\mathrm{v}=\mathrm{bt}^{3} \Rightarrow \mathrm{b}=\frac{\mathrm{LT}^{-1}}{\mathrm{~T}^{3}}=\mathrm{LT}^{-4}$ ,

Asked in: JEE Mains - Units and Dimensions - Test 3

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