Units and Dimensions

Name the physical quantity whose S.I. unit is $\mathrm{J} {\mathrm{C}}^{-1}$. Is it a scalar or a vector quantity?

The density of material in the CGS system of units is $\frac{4g}{{\mathrm{cm}}^3}$. In a system of units in which unit of length is $10 \mathrm{cm}$ and unit of mass is$100 \mathrm{g}$, the value of density of material will be

The density of material in the CGS system of units is  $4 \mathrm{g} {\mathrm{cm}}^{-3}$. In a system of units in which unit of  length is $10 \mathrm{cm}$ and the unit of  mass  is $100 \mathrm{g}$, the value of density of the material will be

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

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 ratio of the dimensions of Planck’s constant and that of the moment of inertia has the dimensions of

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