Dimensional Formulae and Equations

The dimension of $\frac{1}{2}{\epsilon }_0{E}^2$, where  ${\epsilon }_0$ is permittivity of free space and E is electric field, is:

If the dimensions of a physical quantity "Pressure" are given by  $M^a{L}^b{T}^c$ , then the physical quantity will be.

Which two of the following five physical parameters have the same dimensions?
(A) Energy density
(B) Refractive index
(C) Dielectric constant
(D) Young’s modulus
(E) Magnetic field

The dimensions of Planck’s constant are same as

The dimensional formula for magnetic flux is

An equation is given as : $\left(P+\frac{a}{V^2}\right)=b\frac{\theta }{V},$ where $P=\mathrm{Pressure},V=\mathrm{Volume}\mathrm{and}\theta =\mathrm{Absolute}$ temperature. If a and b are constant, then dimensions of ‘a’ will be:

An equation is given as : $\left(P+\frac{a}{V^2}\right)=b\frac{\theta }{V},$ where $P=\mathrm{Pressure},V=\mathrm{Volume}\mathrm{and}\theta =\mathrm{Absolute}$ temperature. If a and b are constant, then dimensions of ‘a’ will be:

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 the constant, called coefficient of viscosity. The dimensional formula of $\eta$ is

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:

Of the following quantities, which one has dimension different from the remaining three?

If $C$ and $R$ denote capacitance and resistance, the dimensional formula of $CR$ 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 for permeability $\mu$ is given by

The dimensional formula for permeability $\mu$ is given by