The potential energy of a particle varies with distance $x$ from a fixed origin as $V = \frac{{A\sqrt x }}{{x + B}}$,where
$A$ and $B$ are constants. The dimensions of $AB$ are
$ML^{5/2} T^{-2}$
$M^1 L^2 T^{-2}$
$M^{3/2} L^{3/2} T^{-2}$
$M^1 L^{7/2} T^{-2}$
Which of the following pair of quantities do not have the same dimensions
The dimensional formula for $r.m.s.$ (root mean square) velocity is
The dimensions of $C{V^2}$ matches with the dimensions of
Young-Laplace law states that the excess pressure inside a soap bubble of radius $R$ is given by $\Delta P=4 \sigma / R$, where $\sigma$ is the coefficient of surface tension of the soap. The EOTVOS number $E_0$ is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of $g$, the acceleration due to gravity $\rho$ the density of the surrounding fluid $\sigma$ and a characteristic length scale $L$ which could be the radius of the bubble. A possible expression for $E_0$ is
$Pascal-Second$ has dimension of