Question
A system has basic dimensions as density $[D]$, velocity $[V]$ and area $[A]$. The dimensional representation of force in this system is
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Answer
$\mathrm{F}=\mathrm{Ma}=$ volume $\times$ density $\times\left(\frac{\mathrm{L}}{\mathrm{T}^{2}}\right)$
$=(\text { Area } \times \text { length }) \times$ density $\times \frac{\mathrm{L}}{\mathrm{T}^{2}}$
$\left[\text { velocity } \mathrm{v}^{2}=\frac{\mathrm{L}^{2}}{\mathrm{T}^{2}}\right]$
$=\left[\mathrm{Av}^{2} \mathrm{D}\right]$
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