Question

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

• A. $\left[\rho v^{4} f^{-3}\right]$
• B. $\left[\rho v^{3} f^{-1}\right]$
• C. $\left[\rho v f^{2}\right]$
• D. $\left[\rho^{2} v^{2} f^{2}\right]$

Answer 1

Answer: (A)

Momentum, $p \propto f^{a} v^{b} \rho^{c}$
$[MLT]=[T] [LT] [ML]$
$\left[ MLT ^{-1}\right]=\left[ M ^{ C } b ^{b-3 C } T ^{- a -b}\right]$
$\Rightarrow c=1$
$b-3 c =1$
$\Rightarrow b =4$
$-a-b =-1$
$a + b =1, a=-3$
$[P] =\left[f^{-3} v^{4} \rho\right]$