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

If ${E}, {L}, {m}$ and ${G}$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of ${P}$ in the formula ${P}={EL}^{2} {m}^{-5} {G}^{-2}$ are

An artificial satellite is revolving around a planet of mass $M$ and radius $R$ in a circular orbit of radius $r$. From Kepler’s third law about the period of a satellite around a common central body, square of the period of revolution $T$ is proportional to the cube of the radius of the orbit $r$. Show using dimensional analysis that $T\, = \,\frac{k}{R}\sqrt {\frac{{{r^3}}}{g}} $, where $k$ is dimensionless constant and $g$ is acceleration due to gravity.

If Surface tension $(S)$, Moment of Inertia $(I)$ and Planck’s constant $(h)$, were to be taken as the fundamental units, the dimensional formula for linear momentum would be