Dimensional Formulae and Equations

Dimensional formula for linear momentum is

Why dimensional methods are applicable only up to three quantities?

If humans were to settle on other planets which of the fundamental quantities will be in trouble? Why?

A quantity $\left(X\right)$ is defined as: $X=\frac{Y}{Z}$. If  $\left[\mathrm{Y}\right]=\left[{\mathrm{MLT}}^{-2}\right]$, $\left[Z\right]=\left[L^2\right]$. Find the dimensions of quantity $\left(\mathrm{X}\right)$. Identify this physical quantity.

The dimensions of pressure are same as that of

Candela is used to express electric field intensity.

Name one dimensional constant.
(Joule's constant/ Universal gas constant)

Dimensional formula for linear momentum is

If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities then the dimensions of length will be

$\mathrm{M}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}$ the units in $\mathrm{C}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n}\mathrm{ }\mathrm{I}$ with their corresponding dimensional formula in $\mathrm{C}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{n}\mathrm{ }\mathrm{I}\mathrm{I}$ .

Which of the following sets have different dimensions?

If $P\mathit{,}\mathit{ }Q\mathit{,}\mathit{ }R$ are three physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?

Choose among the pairs listed below, the one which has the same dimension.

The dimensional formula (in S.I.) of the quantity $\frac{\mathit{L}}{\mathit{C}\mathit{V}\mathit{R}}$ (where $\mathit{C}=$ capacitance, $\mathit{V}=$ voltage & $\mathit{R}=$ resistance)

Select the dimensional formula of $\frac{B^2}{2{\mu }_0}$. Here $B$ is the magnetic field and ${\mu }_0$ is the permeability of the free space.

The dimensional formula of capacitance is _____. Take Q as the dimension formula of charge.

Match the following.
 

The dimensional formula for inductance is

Which of the following equation is dimensionally incorrect?

The dimensional formula of action $=(\mathrm{energy}\times \mathrm{time})$ is