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:

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

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