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Q.

Taking frequency f, velocity (v) and Density (ρ) to be the fundamental quantities then the Dimensional formula for momentum will be

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a

$({ρv}^{3} f^{- 1})$

b

$({ρv}^{4} f)$

c

$({ρvf}^{2})$

d

$(ρ^{2} v^{2} f^{2})$

answer is A.

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Detailed Solution

$P \propto f^{a} v^{b} ρ^{c}; {MLT}^{- 1} = k {[T^{- 1}]}^{a} {[{LT}^{- 1}]}^{b} {[{ML}^{- 3}]}^{c}$ $\Rightarrow a = 1, b = 4 a n d c = 1$

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