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Question Number 94782 by I want to learn more last updated on 21/May/20

$$\mathrm{The}\mathrm{velocity}\mathrm{of}\mathrm{physical}\mathrm{quantities}\mathrm{is}\mathrm{given}\mathrm{by}$$$$\mathrm{v}=\sqrt{\frac{\mathrm{P}+\frac{1}{\mathrm{n}}}{\mathrm{x}}},\mathrm{where}\mathrm{P}\mathrm{is}\mathrm{the}\mathrm{pressure}.$$$$\mathrm{Find}\mathrm{the}\mathrm{dimention}\mathrm{of}\mathrm{n}\mathrm{and}\mathrm{x}.$$

Answered by mr W last updated on 21/May/20

$$v=\left[\frac{m}{s}\right]$$$$p=\left[\frac{N}{m^2}\right]=\frac{1}{n}$$$$\Rightarrow n=\left[\frac{m^2}{N}\right]$$$$\frac{\left[\frac{N}{m^2}\right]}{x}={\left(\left[\frac{m}{s}\right]\right)}^2=\left[\frac{m^2}{s^2}\right]$$$$\Rightarrow x=\left[\frac{N}{m^2}\times \frac{s^2}{m^2}\right]=\left[\frac{kgm}{s^2}\times \frac{s^2}{m^4}\right]=\left[\frac{kg}{m^3}\right]$$$$i.e.xisthedensity.$$

Commented by I want to learn more last updated on 21/May/20

$$\mathrm{I}\mathrm{appeciate}\mathrm{sir}.$$

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