Question

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. $\left[ ML ^{\left.5 / 2 T ^{-2}\right],[ L ]}\right.$
• B. $\left[ MLT ^{-2}\right],\left[ L ^{2}\right]$
• C. $[ L ],\left[ ML ^{3 / 2} T ^{-2}\right]$
• D. $\left[ L ^{2}\right],\left[ MLT ^{-2}\right]$

Answer 1

Answer: (A)

$u=\frac{A \sqrt{x}}{x+B}$
By the principle of homogeneity, $x=B$ (dimensionally)
$\Rightarrow B=[ L ]$
and $\left[ ML ^{2} T ^{-2}\right]=\frac{A L^{1 / 2}}{L}$
$\left[ ML ^{2} T ^{-2}\right]=A L^{-1 / 2}$
$A=\left[ ML ^{3 / 2} T ^{-2}\right]$