The force $F$ on a sphere of radius $'a'$ moving in a medium with velocity $'v'$ is given by $F = 6\pi \eta av$. The dimensions of $\eta $ are

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity $X$ as follows: [position $]=\left[X^\alpha\right] ;[$ speed $]=\left[X^\beta\right]$; [acceleration $]=\left[X^{ p }\right]$; [linear momentum $]=\left[X^{ q }\right]$; [force $]=\left[X^{ I }\right]$. Then -

$(A)$ $\alpha+p=2 \beta$

$(B)$ $p+q-r=\beta$

$(C)$ $p-q+r=\alpha$

$(D)$ $p+q+r=\beta$

The dimensions of pressure are

If e is the electronic charge, $c$ is the speed of light in free space and $h$ is Planck's constant, the quantity $\frac{1}{4 \pi \varepsilon_{0}} \frac{| e |^{2}}{h c}$ has dimensions of .......

If $C$ and $L$ denote capacitance and inductance respectively, then the dimensions of $LC$ are

Let $[{\varepsilon _0}]$ denotes the dimensional formula of the permittivity of the vacuum and $[{\mu _0}]$ that of the permeability of the vacuum. If $M = {\rm{mass}}$, $L = {\rm{length}}$, $T = {\rm{Time}}$ and $I = {\rm{electric current}}$, then