First slide

Dimensions of physical quantities

Question

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

Moderate

A

$[M L^{- 1} T^{- 2}]$
B

$[M^{2} L^{- 2} T^{- 2}]$
C

$[M L^{- 1} T^{0}]$
D

$[M^{2} L^{- 2} T^{- 4}]$

Solution

As,
$\frac{d^{2} s}{d t^{2}}$ is acceleration or $\frac{m}{s^{2}}$ or $[{LT}^{- 2}]$
In the similar way,
$[\frac{d^{2} y}{d x^{2}}] = [\frac{y}{x^{2}}] = \frac{[{ML}^{- 1} T^{- 2}]}{{[T^{- 1}]}^{2}} = [{ML}^{- 1} T^{0}]$

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