Assertion $(A)$: Energy per unit volume and angular momentum can be added dimensionally.
Reason $(R)$: Physical quantities having same dimensions can be added or subtracted.

The entropy of any system is given by
$S = \alpha^{2} \beta \ln \left[\frac{\mu k R}{J \beta^{2}} + 3\right]$
Where $\alpha$ and $\beta$ are constants. $\mu, J, k$ and $R$ are the number of moles,mechanical equivalent of heat,Boltzmann constant,and gas constant respectively. [Take $S = \frac{dQ}{T}$].
Choose the incorrect option from the following:

Which of the following is dimensionally correct?

The expression given below shows the variation of velocity $(v)$ with time $(t)$,$v=At^2+\frac{Bt}{C+t}$. The dimension of $ABC$ is

The dimensional formulas for acceleration,velocity,and length are $\alpha \beta^{-2}$,$\alpha \beta^{-1}$,and $\alpha \gamma$ respectively. What is the dimensional formula for the coefficient of friction?

In a particular system of units,a physical quantity can be expressed in terms of the electric charge $e$,electron mass $m_e$,Planck's constant $h$,and Coulomb's constant $k = \frac{1}{4 \pi \epsilon_0}$,where $\epsilon_0$ is the permittivity of vacuum. In terms of these physical constants,the dimension of the magnetic field is $[B] = [e]^\alpha [m_e]^\beta [h]^\gamma [k]^\delta$. The value of $\alpha + \beta + \gamma + \delta$ is . . . . .