Question

If Frequency F, velocity v, and density D are considered fundamental units, the dimensional formula for momentum will be :

Answer 1

Let's see

Momentum be P

$\\ \rm\Rrightarrow P=[Frequency]^a[velocity]^b[Density]^c$

$\\ \rm\Rrightarrow [P]=[F]^a[v]^b[D]^c$

$\\ \rm\Rrightarrow [M^1L^1T^{-1}]=[T^{-1}]^a[L^1T^{-1}]^b[M^1L^{-3}]^c$

$\\ \rm\Rrightarrow MLT^{-1}=T^{-a}L^bT^{-b}M^cL^{-3c}$

$\\ \rm\Rrightarrow MLT^{-1}=T^{-a-b}L^{b-3c}M^c$

On comaparing

• c=1

So

• b-3c=1
• b-3=1
• b=1+3
• b=4

and

• -a-b=-1
• -a-4=-1
• -a=-1+4=3
• a=-3

So the unit is

• DV⁴/F³

Answer 2

Answer:

(Frequency)⁻³(velocity)⁴Density

Explanation:

See attachments.