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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

$A^{2} vρ$

b

$Avρ$

c

${Avρ}^{2}$

d

${Av}^{2} ρ$

answer is B.

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Detailed Solution

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F = ${kA}^{x} v^{y} ρ^{z}$

$\Rightarrow {MLT}^{- 2} = {[L^{2}]}^{x} {[{LT}^{- 1}]}^{y} {[{ML}^{- 3}]}^{z}$

$\Rightarrow$ z = 1, 2x+y-3z = 1, -y = -2 $\Rightarrow$ y = 2

$\Rightarrow$ x = 1

$F = {kA}^{1} v^{2} ρ^{1} = {Av}^{2} ρ, k = 1$

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