Question

F=kA^2ut find the dimension of k

Answer 1

Answer:

Only quantities with like dimensions may be added(+), subtracted(-) or compared (=,<,>). This rule provides a powerful tool for checking whether or not equations are dimensionally consistent. It is also possible to use dimensional analysis to suggest plausible equations when we know which quantities are involved.

Example of checking for dimensional consistency

Consider one of the equations of constant acceleration,

s = ut + 1/2 at2. (1)

The equation contains three terms: s, ut and 1/2at2. All three terms must have the same dimensions.

s: displacement = a unit of length, L

ut: velocity x time = LT-1 x T = L

1/2at2 = acceleration x time = LT-2 x T2 = L

All three terms have units of length and hence this equation is dimensionally valid. Of course this does not tell us if the equation is physically correct, nor does it tell us whether the constant 1/2 is correct or not.