If orbital velocity of planet is given by $v = {G^a}{M^b}{R^c}$, then
$a = 1/3,\,b = 1/3,\,c = - 1/3$
$a = 1/2,\,b = 1/2,\,c = - 1/2$
$a = 1/2,\,b = - 1/2,\,c = 1/2$
$a = 1/2,\,b = - 1/2,\,c = - 1/2$
The potential energy of a particle varies with distance $x$ from a fixed origin as $U\, = \,\frac{{A\sqrt x }}{{{x^2} + B}}$ Where $A$ and $B$ are dimensional constants then find the dimensional formula for $A/B$
Given that $v$ is speed, $r$ is the radius and $g$ is the acceleration due to gravity. Which of the following is dimensionless
The dimensions of the area $A$ of a black hole can be written in terms of the universal gravitational constant $G$, its mass $M$ and the speed of light $c$ as $A=G^\alpha M^\beta c^\gamma$. Here,
The force $F$ is given in terms of time $t$ and displacement $x$ by the equation $F = A\,cos\,Bx + C\,sin\,Dt.$ The dimensional formulae of $D/B$ is
The Martians use force $(F)$, acceleration $(A)$ and time $(T)$ as their fundamental physical quantities. The dimensions of length on Martians system are