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
$\left[ ML ^{5 / 2} T ^{-2}\right],[ L ]$
$\left[ MLT ^{-2}\right],\left[L^2\right]$
$[L],\left[ ML ^{3 / 2} T ^{-2}\right]$
$\left[L^2\right],\left[ MLT ^{-2}\right]$
In the equation $y = pq$ $tan\,(qt)$, $y$ represents position, $p$ and $q$ are unknown physical quantities and $t$ is time. Dimensional formula of $p$ is
convert $1\; newton$ ($SI$ unit of force) into $dyne$ ($CGS$ unit of force)
A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$
The period of a body under SHM i.e. presented by $T = {P^a}{D^b}{S^c}$; where $P$ is pressure, $D$ is density and $S$ is surface tension. The value of $a,\,b$ and $c$ are
Given that $v$ is the speed, $r$ is radius and $g$ is acceleration due to gravity. Which of the following is dimensionless?