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1.Units, Dimensions and Measurement
medium
જો $y$ દબાણને રજૂ કરે અને $x$ વેગ ઢોળાવને રજૂ કરે, તો પછી $\frac{d^2 y}{d x^2}$ ના પરિમાણો ક્યા હશે?
A$\left[ ML ^{-1} T ^{-2}\right]$
B$\left[ M ^2 L ^{-2} T ^{-2}\right]$
C$\left[ ML ^{-1} T ^0\right]$
D$\left[ M ^2 L ^{-2} T ^{-4}\right]$
Solution
(c)
$\frac{d^2 y}{d x^2}$ will have dimensions of $\frac{y}{x^2}$
$y \rightarrow$ pressure, $x \rightarrow$ velocity gradient
$x \rightarrow \frac{V}{L} \Rightarrow \frac{ LT ^{-1}}{ L } \Rightarrow T ^{-1}$
$\frac{y}{x^2}=\frac{ ML ^{-1} T ^{-2}}{ T ^{-2}} \Rightarrow\left[ ML ^{-1}\right]$
$\frac{d^2 y}{d x^2}$ will have dimensions of $\frac{y}{x^2}$
$y \rightarrow$ pressure, $x \rightarrow$ velocity gradient
$x \rightarrow \frac{V}{L} \Rightarrow \frac{ LT ^{-1}}{ L } \Rightarrow T ^{-1}$
$\frac{y}{x^2}=\frac{ ML ^{-1} T ^{-2}}{ T ^{-2}} \Rightarrow\left[ ML ^{-1}\right]$
Standard 11
Physics
