Which of the following is the dimension of pressure?
A. \(\mathrm{MLT}^2\)
B. \(\mathrm{ML}^{-1} \mathrm{~T}^2\)
C. \(\mathrm{ML}^{-3}\)
D. \(\mathrm{ML}^{-3} \mathrm{~T}^{-2}\)
Correct Answer: B
Explanation
\(\mathrm{ML}^{-1} \mathrm{~T}^{-2}\)
Pressure \(=\frac{\text { Force }}{\text { Area }}\left(\mathrm{N} / \mathrm{m}^2\right)\)
where \(\mathrm{F}(\mathrm{N})=\mathrm{kgm} / \mathrm{s}^2\)
and \(\mathrm{A}\left(\mathrm{m}^2\right)=\mathrm{m}^2\)
thus,
\begin{aligned}
\text { pressure } &=\frac{\mathrm{kgm} / \mathrm{s}^2}{\mathrm{~m}^2}=\frac{\mathrm{kg} / \mathrm{s}^2}{\mathrm{~m}} \\
=\frac{\mathrm{kg}}{\mathrm{ms}^2}=k \mathrm{~kg}^{-1} \mathrm{~s}^{-2}=\mathrm{ML}^{-1} \mathrm{~T}^{-2}
\end{aligned}