Which of the following combinations has the dimension of electrical resistance ( ${ \varepsilon _0}$ is the permittivity of vacuum and ${\mu _0}$ is the permeability of vacuum) ?

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

Choose the most appropriate answer from the options given below:

The dimensional formula for the modulus of rigidity is

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

Einstein’s mass-energy relation emerging out of his famous theory of relativity relates mass $(m)$ to energy $(E)$ as  $E = mc^2$, where $c$ is speed of light in vacuum. At the nuclear level, the magnitudes of energy are very small. The energy at nuclear level is usually measured in $MeV$, where $1\,MeV = 1.6\times 10^{-13}\,J$ ; the masses are measured i unified atomicm mass unit (u) where, $1\,u = 1.67 \times 10^{-27}\, kg$

$(a)$ Show that the energy equivalent of $1\,u$ is $ 931.5\, MeV$.

$(b)$ A student writes the relation as $1\,u = 931.5\, MeV$. The teacher points out that the relation  is dimensionally incorrect. Write the correct relation.

Which two of the following five physical paramenters have the same dimensions $?$ 

$(1) $ energy density

$(2)$ refractive index

$(3) $ dielectric constant

$(4) $ Young's modulus

$(5)$ magnetic field