Derivation of expression for Centripetal Force.

Since force is not the fundamental quantity, write it's dimensions,

F = ma = (mass)(acceleration)

[F] = [M] [LT] ^-2

[M] [LT] ^-2 = [M]^a [L]^b [LT ^-1]^c

Comparing the exponents of each base quantity, on both sides, and equating,

M : a = 1

L : b + c = 1

T:  -c = -2

a = 1; c = 2; b = -1

Hence F = kmv²/r

and as we know the propotionality constant k = 1.

F = mv²/r

Regards,

Team,

TopperLearning.