$A$ 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 . . . . . . .

To find the distance $d$ over which a signal can be seen clearly in foggy conditions,a railway engineer uses dimensional analysis and assumes that the distance depends on the mass density $\rho$ of the fog,intensity (power/area) $S$ of the light from the signal,and its frequency $f$. The engineer finds that $d$ is proportional to $S^{1/n}$. The value of $n$ is:

The foundations of dimensional analysis were laid down by

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

In a practical unit system,if the unit of mass becomes double and that of time becomes half,then $8 \text{ joule}$ will be equal to .............. unit of work.

If velocity $v$,acceleration $A$,and force $F$ are chosen as fundamental quantities,then the dimensional formula of angular momentum in terms of $v, A$,and $F$ would be