Question Number 29217 by NECx last updated on 05/Feb/18
$${The}\:{velocity}\:{of}\:{a}\:{physical}\:{system} \\ $$$${is}\:{given}\:{by}\:{V}=\left\{\sqrt{\left({p}+\mathrm{1}/{n}\right)}\right\}/{x} \\ $$$${where}\:{p}={pressure}.\:{Find}\:{the} \\ $$$${dimensions}\:{of}\:{n}\:{and}\:{x} \\ $$
Answered by ajfour last updated on 05/Feb/18
![(m^2 /s^2 )⇔((kg/(ms^2 ))/([x]^2 )) [x]= M^( 1/2) L^(−3/2) [n]=M^( −1) LT^( 2) .](Q29229.png)
$$\frac{{m}^{\mathrm{2}} }{{s}^{\mathrm{2}} }\Leftrightarrow\frac{{kg}/\left({ms}^{\mathrm{2}} \right)}{\left[{x}\right]^{\mathrm{2}} } \\ $$$$\left[{x}\right]=\:{M}^{\:\mathrm{1}/\mathrm{2}} {L}^{−\mathrm{3}/\mathrm{2}} \\ $$$$\left[{n}\right]={M}^{\:−\mathrm{1}} {LT}^{\:\:\mathrm{2}} \:\:. \\ $$