If $E, M, J$ and $G$ respectively denote energy, mass, angular momentum, and universal gravitational constant, the quantity which has the same dimensions as the dimensions of $\frac{E J^2}{M^5 G^2}$ is:

Given that $v$ is the speed,$r$ is the radius,and $g$ is the acceleration due to gravity. Which of the following is dimensionless?

If $\text{force} = \frac{\alpha}{\text{density} + \beta^3}$,then the dimensional formulae of $\alpha$ and $\beta$ are respectively:

Young-Laplace law states that the excess pressure inside a soap bubble of radius $R$ is given by $\Delta P = 4 \sigma / R$,where $\sigma$ is the coefficient of surface tension of the soap. The $EOTVOS$ number $E_0$ is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of $g$ (acceleration due to gravity),$\rho$ (density of the surrounding fluid),$\sigma$ (surface tension),and a characteristic length scale $L$ (radius of the bubble). $A$ possible expression for $E_0$ is:

If force $[F]$,acceleration $[A]$,and time $[T]$ are chosen as the fundamental physical quantities,find the dimensions of energy.

Planck's constant $h$,speed of light $c$,and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are):
$(A)$ $M \propto \sqrt{c}$
$(B)$ $M \propto \sqrt{G}$
$(C)$ $L \propto \sqrt{h}$
$(D)$ $L \propto \sqrt{G}$