What is Dimensional Analysis ? State uses of Dimensional Analysis.
A method of obtaining the solution of certain problems in physics by using dimensional formula is called dimensional analysis.
Uses of Dimensional Analysis :
$(a)$ To obtain the relation between the units of some physical quantity in two different systems of units.
$(b)$ To check the dimensional consistency of an equation connecting different physical quantities.
$(c)$ To derive the equation for a physical quantity in terms of the other (related) physical quantities.
Write the dimensions of $a/b$ in the relation $P = \frac{{a - {t^2}}}{{bx}}$ , where $P$ is pressure, $x$ is the distance and $t$ is the time
$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $AD = C\, ln\, (BD)$ holds true. Then which of the combination is not a meaningful quantity ?
If $R , X _{ L }$. and $X _{ C }$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:
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
The foundations of dimensional analysis were laid down by