If y represents pressure and x represents velocity gradient, then… - Vidyadip

MCQ

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
$\left[ M ^2 L ^{-2} T ^{-2}\right]$
✓
$\left[ ML ^{-1} T ^0\right]$
D
$\left[ M ^2 L ^{-2} T ^{-4}\right]$

✓

Answer

Correct option: C.

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

c
(c)

$\frac{d^2 y}{d x^2}$ will have dimensions of $\frac{y}{x^2}$

$y \rightarrow$ pressure, $x \rightarrow$ velocity gradient

$x \rightarrow \frac{V}{L} \Rightarrow \frac{ LT ^{-1}}{ L } \Rightarrow T ^{-1}$

$\frac{y}{x^2}=\frac{ ML ^{-1} T ^{-2}}{ T ^{-2}} \Rightarrow\left[ ML ^{-1}\right]$

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