If the orbital velocity of a planet is given by $v = G^a M^b R^c$,then:

If $L$,$C$,and $R$ denote the inductance,capacitance,and resistance respectively,the dimensional formula for $C^{2}LR$ is

Planck's constant $(h)$,speed of light in vacuum $(c)$,and Newton's gravitational constant $(G)$ are three fundamental constants. Which of the following combinations of these has the dimension of length?

The equation of state of a real gas is given by $(P+\frac{a}{V^2})(V-b)=RT$,where $P, V$ and $T$ are pressure,volume and temperature respectively and $R$ is the universal gas constant. The dimensions of $\frac{a}{b^2}$ are similar to that of:

In the $CGS$ system, the magnitude of the force is $100 \ dynes$. In another system where the fundamental physical quantities are $kilogram$, $meter$, and $minute$, the magnitude of the force is:

The speed of light $(c)$,gravitational constant $(G)$,and Planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be