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  4. If v=(A/t)+Bt2+Ct3 where v is velocity, t is time and A, B and C are constants, then the dimensional formula of B is

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Q. If $v=\frac{A}{t}+Bt^{2}+Ct^{3}$ where $v$ is velocity, $t$ is time and $A, \, B$ and $C$ are constants, then the dimensional formula of $B$ is

NTA AbhyasNTA Abhyas 2022

Solution:

Dimension of velocity = $\left[\right.M^{0}L^{1}T^{- 1}\left]\right.$
$\left[\right. v \left]\right. = \left[\right. B t^{2} \left]\right.$
$\therefore \left[\right. B \left]\right. = \frac{\left[\right. v \left]\right.}{\left[\right. t^{2} \left]\right.} = \frac{\left[\right. \text{M}^{0} \text{L}^{1} \text{T}^{- 1} \left]\right.}{\left[\right. \text{T}^{2} \left]\right.} = \left[\right. \text{L}^{1} \text{T}^{- 3} \left]\right.$