In a new system of units,energy $(E)$,density $(d)$,and power $(P)$ are taken as fundamental units. Then the dimensional formula of the universal gravitational constant $G$ will be .......

Force is given by the expression, $F = A \cos(Bx) + C \cos(Dt)$, where $x$ is displacement and $t$ is time. The dimension of $\left(\frac{D}{B}\right)$ is the same as that of

In the equation $S = a + bt + ct^2$,where $S$ is measured in metres and $t$ is measured in seconds,the unit of $c$ is:

The energy $(E)$, angular momentum $(L)$, and universal gravitational constant $(G)$ are chosen as fundamental quantities. The dimensions of the universal gravitational constant in the dimensional formula of Planck's constant $(h)$ is

$A$ great physicist of this century ($P.A.M.$ Dirac) loved playing with numerical values of fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics ($c, e,$ mass of electron, mass of proton) and the gravitational constant $G$, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe ($\approx 15$ billion years). From the table of fundamental constants in this book, try to see if you too can construct this number. If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants?

$A$ new system of units is proposed in which the unit of mass is $\alpha \ kg$,the unit of length is $\beta \ m$,and the unit of time is $\gamma \ s$. How much will $5 \ J$ measure in this new system?