The equation $\frac{{dV}}{{dt}} = At - BV$ is describing the rate of change of velocity of a body falling from rest in a resisting medium. The dimensions of $A$ and $B$ are
$LT^{-3}, T$
$LT^{-3}, T^{-1}$
$LT, T$
$LT, T^{-1}$
Consider the following equation of Bernouilli’s theorem. $P + \frac{1}{2}\rho {V^2} + \rho gh = K$ (constant)The dimensions of $K/P$ are same as that of which of the following
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.
A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta $. After some time the velocity of the ball attains a constant value known as terminal velocity ${v_T}$. The terminal velocity depends on $(i)$ the mass of the ball $m$, $(ii)$ $\eta $, $(iii)$ $r$ and $(iv)$ acceleration due to gravity $g$. Which of the following relations is dimensionally correct
If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express mass, length and time in terms of dimensions of these quantities.