Question

What is the dimension of the physical quantity$\left(\alpha \right)$ in the equation, $P=\frac{\text{density}}{\alpha }$, where $P$ is the pressure ?

• A. ${\text{L}}^{-2}{\text{T}}^2$
• B. $\text{M}{\text{L}}^4{\text{T}}^{-2}$
• C. $\text{M}{\text{L}}^2{\text{T}}^{-1}$
• D. ${\text{L}}^{-3}{\text{T}}^2$

Answer 1

The correct option is A ${\text{L}}^{-2}{\text{T}}^2$

Given:
$P=\frac{\rho }{\alpha }$
$\Rightarrow \alpha =\frac{\sigma }{P}=\frac{\left[\text{M}{\text{L}}^{-3}\right]}{\left[\text{M}\text{L}{\text{T}}^{-2}\right]}\times \left[{\text{L}}^2\right]=\left[{\text{L}}^{-2}{\text{T}}^2\right]$
Hence, option $\left(D\right)$ is correct.