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Dimensional Analysis

α =F/v2sin β ...

Question

$α = \frac{F}{v^{2}} sin (β t)$ (here v = velocity, F = force, t = time)
Find the dimension of $α$ and $β$

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Solution

$α = \frac{F}{v^{2}} sin (β t)$
dimensionless dimensionless $\Rightarrow$ $[β] [t] = 1 = [β] = [T^{- 1}]$
So $[α] = \frac{[F]}{V^{2}} = \frac{[M^{1} L^{1} T^{- 2}]}{[L^{1} T^{- 1}]^{2}} = M^{1} L^{- 1} T^{0}$

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