The value of a force is $36$units in a system having $\mathrm{metre}$, $\mathrm{Kilogram}$ and $\mathrm{minute}$ as fundamental units. What will be its value in $\mathrm{CGS}$ system?

The unit of work is $\mathrm{Joule} \left(\mathrm{J}\right)$ in the SI system and $\mathrm{erg}$ in the CGS system. Find number of $\mathrm{ergs}$ in $1 \mathrm{Joule}$.

Express $1 \mathrm{MW}\left(\mathrm{megawatt}\right)$ power in a system whose fundamental units are $10 \mathrm{Kg}$, $1 \mathrm{dm}\left(\mathrm{decimetre}\right)$ and $1 \mathrm{minute}$.

Express $1$ atmospheric pressure$(={10}^5 {\mathrm{Nm}}^{-2})$ in CGS system.

Using the method of dimensions, check the correctness of the following equations:

$v=u+at, s=ut+\frac{a{t}^2}{2}$and $v^2-u^2=2as$ where $s$ is the distance travelled by a particle in uniform acceleration $a$ in time $t$, $u$and $v$ are initial and final velocities respectively.

Using the method of dimensions, check the correctness of the following equations:

$\mathrm{K}=\frac{{\mathrm{mv}}^2}{2}$ where $\mathrm{K}$ is the kinetic energy of a body of mass $\mathrm{m}$ moving with velocity $\mathrm{v}$.

Using the method of dimensions, check the correctness of the following equations:

$Fs=\frac{m{v}^2}{2}-\frac{m{u}^2}{2}$where $s$ is the distance moved by a body of mass $m$ acted upon by a force $F$, $u$ and $v$ being respectively the initial and the final velocities of the body.

Using the method of dimensions, check the correctness of the following equations:

$K=\frac{I{\omega }^2}{2}$where $K$ is the rotational kinetic energy, $I$ is the moment of inertia and $\omega$ is the angular velocity of a body rotating about an axis.

Using the method of dimensions, check the correctness of the following equations:

$\rho =\frac{3g}{4{\mathrm{\pi R}}_{\mathrm{e}}\mathrm{G}}$, where $\rho$ is the density and $R_e$ is the radius of the earth.