Given a charge $q$,current $I$ and permeability of vacuum $\mu_0$. Which of the following quantity has the dimension of momentum?

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

Check that the ratio $ke^{2} / G m_{e} m_{p}$ is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

Write the dimensions of $a / b$ in the relation $P = \frac{a - t^2}{bx}$; where $P$ is the pressure,$x$ is the distance,and $t$ is the time.

Consider an expression $Q V = k P T L^\alpha$ where $V, P, T, L$ are volume, pressure, time, and length respectively. The quantity $[Q]$ has dimension $M L^{-1} T^{-1}$. $k$ is a dimensionless constant. The value of the integer $\alpha$ is:

$A$ ball of radius $r$ and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time $t$, given by $t = A \rho^{a} r^{b} \eta^{c} \sigma^{d}$, where $A$ is a constant and $a, b, c, d$ are integers. The value of $\frac{b+c}{a+d}$ is . . . . . . .