Principle of Homogeneity of dimensions and its use?

Question

can anyone explain to me the principle of Homogeneity of dimensions and its use..not really clear about it!..tq..

Answer 1

The dimensions of the physical quantities on the left hand side of an equation must be the same as that on the right hand side

Simple put you cannot subtract one banana from three apples

Dimensional Analysis is a very useful method of confirming the correctness of physical equations

For example take the equation of motion

D = ut + 1/2 a*t^2 (D = distance, u = initial velocity, a = acceleration, t = time)

We can confirm if this is correct by substituting the variables D, u, a and t by their diemensions onl

D = meters (M), u = meters/sec (M/S), a = meters per second squared M/S^2, t = seconds (S)

So we have

M = (M/S)*S + (M/S^2)*S^2

The seconds cancel out and all parts of the equation are now in meters so we can add them up

So, in short , three bananas = 2 bananas + 1 banana