Question

If $V=\sqrt{\frac{\gamma \mathrm{P}}{\rho}},$ then dimensions of $\gamma$ are:

• A. $\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]$
• B. $\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right]$
• C. $\left[\mathrm{M}^{-1} \mathrm{L}^{0} \mathrm{~T}^{0}\right.]$
• D. $\left[\mathrm{M}^{0} \mathrm{L}^{1} \mathrm{T}^{0}\right]$

Answer 1

Answer: (A)

$\begin{aligned} &\text { } \mathrm{V}=\sqrt{\frac{\gamma \mathrm{P}}{\rho}} \text { or } \gamma=\frac{\mathrm{V}^{2} \rho}{\mathrm{P}}\\ &[\gamma]=\frac{\left[\mathrm{LT}^{-1}\right]^{2}\left[\mathrm{ML}^{-3}\right]}{\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]}=\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right] \end{aligned}$