Dimensional Analysis and Physical Equations

Flashcards covering applications of dimensional analysis including checking equation correctness, finding physical constant dimensional formulas, and setting up equation derivations.

Dimensional Formula of Gravitational Constant ($G$)

The dimensional formula for the gravitational constant $G$, derived using $G = \frac{F \times d^2}{M_1 M_2}$, which evaluates to $[M^{-1} L^3 T^{-2}]$.

Dimensional Formula of Force ($F$)

The dimensional representation of force as used in deriving physical constants, given as $[M L T^{-2}]$.

Checking Dimensional Correctness

An application of dimensional analysis that compares the dimensions of the L.H.S and R.H.S of an equation, as shown by testing $V^2 = U^2 + 2a^2s$ where L.H.S $[L^2 T^{-2}]$ does not equal R.H.S $[L^2 T^{-2}] + 2 [L^3 T^{-2}]$.

Simple Pendulum Time Period Dependencies

In deriving physical equations using dimensional analysis, the time period ($t$) of a simple pendulum is considered to depend on mass ($m$), length ($l$), and acceleration due to gravity ($g$), written as $t \propto m^a$, $t \propto l^b$, and $t \propto g^c$.