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Q.

If area (A) velocity (v) and density ( $ρ$ ) are base units, then the dimensional formula of force can be represented as

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a

$A v ρ$

b

$A v ρ^{2}$

c

$A v^{2} ρ$

d

$A^{2} v ρ$

answer is B.

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Detailed Solution

$\begin{array}{l} F = k A^{x} v^{y} ρ^{z} \\ \Rightarrow M L T^{- 2} = {[L^{2}]}^{x} {[L T^{- 1}]}^{y} {[M L^{- 3}]}^{z} \\ \Rightarrow z = 1, 2 x + y - 3 z = 1, - y = - 2 \Rightarrow y = 2 \\ \Rightarrow x = 1 \\ F = k A^{1} v^{2} ρ^{1} = A v^{2} ρ, k = 1 \end{array}$

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If area (A) velocity (v) and density (ρ) are base units, then the dimensional formula of force can be represented as