Question
Calculate the dimensions of force and impulse taking velocity, density and frequency as basic quantities.
✓
Answer
$
v=LT^{-1}, \rho=ML^{-3}, v=T^{-1}
$
Solving for $M , L$ and T in terms of $v , \rho$ and $v$, we get
$
\begin{aligned}
& T=v^{-1}, L=v \nu^{-1} l, M=\rho v^3 \nu^{-3} \\
& \text { [Force] }=MLT^{-2}=\rho v^3 \nu^{-3} v \nu^{-1} v^2=\rho v^4 \nu^{-2} \\
& \text { [Impulse] = Force } \times \text { time }=\rho v^4 \nu^{-2} v^{-1}=\rho v^4 \nu^{-3}
\end{aligned}
$
v=LT^{-1}, \rho=ML^{-3}, v=T^{-1}
$
Solving for $M , L$ and T in terms of $v , \rho$ and $v$, we get
$
\begin{aligned}
& T=v^{-1}, L=v \nu^{-1} l, M=\rho v^3 \nu^{-3} \\
& \text { [Force] }=MLT^{-2}=\rho v^3 \nu^{-3} v \nu^{-1} v^2=\rho v^4 \nu^{-2} \\
& \text { [Impulse] = Force } \times \text { time }=\rho v^4 \nu^{-2} v^{-1}=\rho v^4 \nu^{-3}
\end{aligned}
$
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