The Dimension o f Young Modulus E is shown as;
Nm2=kgms2m2=kgs2m\frac{N}{m^2}=\frac{kgm}{s^2m^2}=\frac{kg}{s^2m}m2N=s2m2kgm=s2mkg
This means that;
(kgs2m)α(kgm3)β(m)γ=ms(\frac{kg}{s^2m})^\alpha (\frac{kg}{m^3})\beta (m)^\gamma=\frac{m}{s}(s2mkg)α(m3kg)β(m)γ=sm
Hence; α=0.5=−βandγ=0\alpha=0.5=-\beta and \gamma=0α=0.5=−βandγ=0
Consequently;
v=Eρv=\sqrt\frac{E}{\rho}v=ρE
i.e ρ\rhoρ is the Density
Answer: v=Eρv=\sqrt\frac{E}{\rho}v=ρE
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