Dimensions of Physical Quantities and Dimensional Analysis

According to Newton, the viscous force acting between liquid layers of area A and velocity gradient  $\frac{\Delta v}{\Delta z}$ is given by $F=-\eta A\frac{\Delta v}{\Delta z}$, where $\eta$ is constant called coefficient of viscosity. The dimensional formula of $\eta$ is:

If $\text{C}$ and $\text{R}$ denote capacitance and resistance respectively, then the dimensional formula of $\text{CR}$ is

Turpentine oil is flowing through a tube of length $l$ and radius r. The pressure difference between the two ends of the tube is p. The viscosity of oil is given by

                         $\eta =\frac{p\left(r^2-x^2\right)}{\mathrm{}\mathrm{}\mathrm{}4vl}$

Where $v$ is the velocity of oil at a distance $x$ from the axis of the tube. The dimensions of  $\eta$ are:

The dimensional formula of the constant $a$ in Vander Waal’s gas equation  $\left(P+\frac{a}{V^2}\right)(V-b)=RT$  is:

The dimensional formula of the constant $a$ in Vander Waal’s gas equation  $\left(P+\frac{a}{V^2}\right)(V-b)=RT$  is:

Pressure depends on distance as $P=\alpha \beta \exp \left(-\alpha zk\theta \right)$, where $\alpha ,\beta$ are constants $z$ is distance, $k$ is Boltzman's constants and $\theta$ is temperature. The dimension of $\beta$ are

The units of force and length are made three times of their earlier values. Earlier the energy of energy of the system was $81 \mathrm{J}$. What will be the energy of the same system in new units?

Planck's constant has the dimension of

Dimensions of 'ohm' are same as

If speed of light $c$, acceleration due to gravity $g$ and pressure $p$ are taken as fundamental units, the dimensions of gravitational constant $G$ are

The speed of light $c$, gravitational constant $G$, and Planck's constant $h$ are taken as the fundamental units in a system. The dimension of time in this new system should be,

The pair(s) of physical quantities that have same dimension, is (are):

The dimensions of the quantities in one (or more) of the following pairs are the same. Identify the pair(s).

$L, C\text{ and }R$ represent the physical quantities, inductance, capacitance and resistance, respectively. The combinations which have the dimensions of frequency are

Which of the following physical quantities have the same dimensions ?

Which of the following quantities has the S.I. unit $\mathrm{kg} {\mathrm{m}}^2 {\mathrm{s}}^{-3} {\mathrm{A}}^{-2}$?