Answer to Question #174386 in Mechanics | Relativity for Prosper Nwawo

Question

The velocity of a physical system is given by v=[{p+1/n}/x]½.

Where p is the pressure, find the dimensions of n and x.

Answer 1

Solution.

$v=\sqrt{\frac{p+\frac{1}{n}}{x}};$ $[v]=1ms^{-1};$ $p=\frac{F}{s};$ $[p]=1Nm^{-2};$

$[F]=1N=1kgms^{-2};$

$[\frac{1}{n}]=1Nm^{-2};\implies [n]=1N^{-1}m^{2}=1kg^{-1}m^{-1}s^2m^{2}= 1kg^{-1}ms^2;$ $x=\frac{p+\frac{1}{n}}{v^2};$ $[x]=\frac{1Nm^{-2}}{1m^2s^{-2}}=1Nm^{-4}s^2=1kgms^{-2}m^{-4}s^{2}=1kgm^{-3};$

Answer: $[n]=1kg^{-1}ms^2; [x]=1kgm^{-3}.$