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1.Units, Dimensions and Measurement

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The potential energy $u$ of a particle varies with distance $x$ from a fixed origin as $u=\frac{A \sqrt{x}}{x+B}$, where $A$ and $B$ are constants. The dimensions of $A$ and $B$ are respectively

A

$\left[ ML ^{5 / 2} T ^{-2}\right],[ L ]$

B

$\left[ MLT ^{-2}\right],\left[L^2\right]$

C

$[L],\left[ ML ^{3 / 2} T ^{-2}\right]$

D

$\left[L^2\right],\left[ MLT ^{-2}\right]$

Solution

(a)

$u=\frac{A \sqrt{x}}{x+B}$

By the principle of homogeneity, $x=B$ (dimensionally)

$\Rightarrow B=[L]$

$\text { and }\left[ ML ^2 T ^{-2}\right]=\frac{A L^{1 / 2}}{L}$

${\left[ ML ^2 T ^{-2}\right]=A L^{-1 / 2}}$

$A=\left[ ML ^{3 / 2} T ^{-2}\right]$

Std 11

Physics

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