Question

If $y$ represents pressure and $x$ represents velocity gradient, then the dimensions of $\frac{d^{2} y}{d x^{2}}$ are

• A. $\left[ ML ^{-1} T ^{-2}\right]$
• B. $\left[ M ^{2} L ^{-2} T ^{-2}\right]$
• C. $\left[ ML ^{-1} T ^{0}\right]$
• D. $\left[ M ^{2} L^{-2} T ^{-4}\right]$

Answer 1

Answer: (C)

$\frac{d^{2} y}{d x^{2}}$ will have dimensions of $\frac{y}{x^{2}}$
$y \rightarrow$ pressure, $x \rightarrow$ velocity gradient
$x \rightarrow \frac{V}{L} \Rightarrow \frac{L T^{-1}}{L} \Rightarrow T^{-1}$
$\frac{y}{x^{2}}=\frac{M L^{-1} T^{-2}}{T^{-2}} \Rightarrow \left[ ML ^{-1}\right]$