Question

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

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

Answer 1

Answer: (C)

$\left[M{L}^{-1}{T}^0\right]$

Dimensions of $\frac{d^{2}y}{d{x}^2}$ = dimension of $\frac{y}{x^2}$

Dimension of y $M{L}^{-1}{T}^{-2}$

Dimension of x $T^{-1}$

$\frac{d^{2}y}{d{x}^2}=\frac{M{L}^{-1}{T}^{-2}}{{\left(T^{-1}\right)}^2}=M{L}^{-1}{T}^0$