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

Question

Taking frequency f, velocity v and density ρ to be the fundamental quantities, then the dimensional formula for momentum will be (A) [ρ v4 f-3] (B) [ρ v3 f-1] (C) [ρ v f2] (D) [ρ2 v2 f2]

Tardigrade Admin · Accepted Answer

Momentum, p propto fa vb ρc [MLT]=[T] [LT] [ML] [ MLT -1]=[ M C b b-3 C T - a -b] ⇒ c=1 b-3 c =1 ⇒ b =4 -a-b =-1 a + b =1, a=-3 [P] =[f-3 v4 ρ]

Q. Taking frequency $f$ , velocity $v$ and density $ρ$ to be the fundamental quantities, then the dimensional formula for momentum will be

$[ρ v^{4} f^{- 3}]$

$[ρ v^{3} f^{- 1}]$

$[ρ v f^{2}]$

$[ρ^{2} v^{2} f^{2}]$

Momentum, $p \propto f^{a} v^{b} ρ^{c}$
$[M L T] = [T] [L T] [M L]$
$[M L T^{- 1}] = [M^{C} b^{b - 3 C} T^{- a - b}]$
$\Rightarrow c = 1$
$b - 3 c = 1$
$\Rightarrow b = 4$
$- a - b = - 1$
$a + b = 1, a = - 3$
$[P] = [f^{- 3} v^{4} ρ]$

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

[ρv4f−3]

[ρv3f−1]

[ρvf2]

[ρ2v2f2]