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

Given below are two statements: One is labelled as Assertion $(A)$ and other is labelled as Reason $(R)$.
Assertion $(A)$: Time period of oscillation of a liquid drop depends on surface tension $(S)$,if density of the liquid is $\rho$ and radius of the drop is $r$,then $T = k \sqrt{\rho r^{3} / S}$ is dimensionally correct,where $k$ is dimensionless.
Reason $(R)$: Using dimensional analysis,we find that the $R.H.S.$ has different dimensions than that of the time period.

The density of a material in the $CGS$ system of units is $4\,g/cm^3$. In a system of units in which the unit of length is $10\,cm$ and the unit of mass is $100\,g$,the value of the density of the material will be:

If the velocity of light $c$,universal gravitational constant $G$,and Planck's constant $h$ are chosen as fundamental quantities,the dimensions of mass in the new system are:

$E, m, L, G$ represent energy,mass,angular momentum,and gravitational constant respectively. The dimensions of $\frac{EL^2}{m^5 G^2}$ will be that of

Find the dimensional formula of $\frac{a}{b}$ in the equation $F=a \sqrt{x}+b t^2$,where $F$ is force,$x$ is distance,and $t$ is time.