If y represents pressure and x represents velocity gradient, then the dimensions of (d2 y/d x2) are

Question

If y represents pressure and x represents velocity gradient, then the dimensions of (d2 y/d x2) are (A) [ ML -1 T -2] (B) [ M 2 L -2 T -2] (C) [ ML -1 T 0] (D) [ M 2 L-2 T -4]

Tardigrade Admin · Accepted Answer

(d2 y/d x2) will have dimensions of (y/x2) y arrow pressure, x arrow velocity gradient x arrow (V/L) ⇒ (L T-1/L) ⇒ T-1 (y/x2)=(M L-1 T-2/T-2) ⇒ [ ML -1]

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

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

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

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

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

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

Q. If y represents pressure and x represents velocity gradient, then the dimensions of dx2d2y​ are

[ML−1T−2]

[M2L−2T−2]

[ML−1T0]

[M2L−2T−4]