Question

If frequency $F$, velocity $V$, and density $D$ are considered fundamental units, the dimensional formula for momentum will be

• A. $DV{F}^2$
• B. $D{V}^2{F}^{-1}$
• C. $D^2{V}^2{F}^2$
• D. $D{V}^4{F}^{-3}$

Answer 1

The correct option is D $D{V}^4{F}^{-3}$

Momentum $=\left[F{]}^a\right[V{]}^b[D{]}^c$

$⟹\left[ML{T}^{-1}\right]=\left[T^{-1}{]}^a\right[L{T}^{-1}{]}^b[M{L}^{-3}{]}^c$

Comparing both sides,

$c=1$

$b-3c=1$

$\therefore b=4$

Also,

$a+b=1$

$\therefore a=-3$

Therefore,

Momentum $=\left[F{]}^{-3}\right[V{]}^4[D{]}^1=D{V}^4{F}^{-3}$