If force $(F)$, length $(L)  $ and time $(T)$ are assumed to be fundamental units, then the dimensional formula of the mass will be

In a particular system of units, a physical quantity can be expressed in terms of the electric charge $c$, electron mass $m_c$, 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 $[B]=[c]^\alpha\left[m_c\right]^\beta[h]^\gamma[k]^\delta$. The value of $\alpha+\beta+\gamma+\delta$ is. . . . .

If dimensions of critical velocity $v_c$ of a liquid flowing through a tube are expressed as$ [\eta ^x \rho ^yr^z]$ where  $\eta ,\rho $ and $r $ are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of $x, y$ and $z$ are given by

A famous relation in physics relates 'moving mass' $m$ to the 'rest mass' $m_{0}$ of a particle in terms of its speed $v$ and the speed of light, $c .$ (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant $c$. He writes:

$m=\frac{m_{0}}{\left(1-v^{2}\right)^{1 / 2}}$

Guess where to put the missing $c$

From the equation $\tan \theta = \frac{{rg}}{{{v^2}}}$, one can obtain the angle of banking $\theta $ for a cyclist taking a curve (the symbols have their usual meanings). Then say, it is

The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right)\,(V - b) = RT$. Here $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature and $a,\,b,\,R$ are constants. The dimensions of $'a'$ are