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Q.

Taking frequency f, velocity v and density r to be the fundamental quantities, then the dimensional formula for momentum will be

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a

[ρv4f−3]

b

[ρv3f−1]

c

[ρvf2]

d

[ρ2v2f2]

answer is A.

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Detailed Solution

Momentum, p∝favbρc[MLT−1]=[T−1]a[LT−1]b[ML−3]c[MLT−1]=[McLb−3cT−a−b]⇒c=1b−3c=1⇒b=4−a−b=−1a+b=1,  a=−3[P]=[f−3v4ρ]
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Taking frequency f, velocity v and density r to be the fundamental quantities, then the dimensional formula for momentum will be