If the speed of light $(c)$,acceleration due to gravity $(g)$,and pressure $(p)$ are taken as the fundamental quantities,then the dimension of the gravitational constant $(G)$ is:

If velocity $(V)$,force $(F)$ and time $(T)$ are chosen as fundamental quantities,then the dimensions of energy are:

The number of particles crossing a unit area perpendicular to the $X$-axis in unit time is given by $n = -D \frac{n_2 - n_1}{x_2 - x_1}$,where $n_1$ and $n_2$ are the number of particles per unit volume at positions $x_1$ and $x_2$ respectively. Find the dimensions of $D$,which is known as the diffusion constant.

The time dependence of a physical quantity $P$ is given by $P = P_0 e^{-\alpha t^2}$,where $\alpha$ is a constant and $t$ is the time. Then the constant $\alpha$ has:

The amount of heat energy $Q$ used to heat up a substance depends on its mass $m$,its specific heat capacity $s$,and the change in temperature $\Delta T$ of the substance. Using the dimensional method,find the expression for $s$. (Given that $[s] = [L^2 T^{-2} K^{-1}]$)

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?