Force $F$ is given by the equation $F = \frac{X}{\text{Linear density}}$. Then the dimensions of $X$ are:

Density of a liquid in $CGS$ system is $0.625 \ g/cm^3$. What is its magnitude in $SI$ system?

If $C$ (the velocity of light), $h$ (Planck's constant), and $G$ (gravitational constant) are taken as fundamental quantities, then the dimensional formula of mass is

$A$ ball of radius $r$ and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time $t$, given by $t = A \rho^{a} r^{b} \eta^{c} \sigma^{d}$, where $A$ is a constant and $a, b, c, d$ are integers. The value of $\frac{b+c}{a+d}$ 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

The force $F$ is given by the equation $F = at + bt^2$,where $t$ is time. What are the dimensions of $a$ and $b$?