The pair of physical quantities not having the same dimensions is:

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(A)$ Mass density	$(I)$ $[ML^2T^{-3}]$
$(B)$ Impulse	$(II)$ $[MLT^{-1}]$
$(C)$ Power	$(III)$ $[ML^2T^0]$
$(D)$ Moment of inertia	$(IV)$ $[ML^{-3}T^0]$

Choose the correct answer from the options given below:

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

It is estimated that each $cm^2$ of Earth receives about $2 \text{ calorie}$ of heat energy per minute from the Sun. This is called the solar constant. The value of the solar constant in $S.I.$ units is:

The density of water is $1000 \; kg \; m^{-3}$. The density of water vapour at $100^{\circ} C$ and $1 \; atm$ pressure is $0.6 \; kg \; m^{-3}$. The volume of a molecule multiplied by the total number gives what is called molecular volume. Estimate the volume of a water molecule.

Dimensions of the quantity $\frac{p}{\varepsilon_0 \mu_0}$, where $p$ is the pressure, $\varepsilon_0$ is the electric permittivity of free space, and $\mu_0$ is the permeability of free space, will be: