The dimension of $\frac{\mathrm{B}^{2}}{2 \mu_{0}}$, where $\mathrm{B}$ is magnetic field and $\mu_{0}$ is the magnetic permeability of vacuum, is

Dimensions of coefficient of viscosity are

Given below are two statements: One is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion $A$ : Product of Pressure $(P)$ and time $(t)$ has the same dimension as that of coefficient of viscosity.

Reason $R$ : Coefficient of viscosity $=\frac{\text { Force }}{\text { Velocity gradient }}$

Question : Choose the correct answer from the options given below 

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.

The period of a body under SHM i.e. presented by $T = {P^a}{D^b}{S^c}$; where $P$ is pressure, $D$ is density and $S$ is surface tension. The value of $a,\,b$ and $c$ are

The dimensions of $emf$ in $MKS$ is