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If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are


 Let mass mFaVbTc or m=kFaVbTc

where k is a dimensionless constant and a, 19 and c are the exponents. Writing dimensions on both sides, we get ML0T0=MLT2aLT1b[T]cML0T0=MaLa+bT2ab+c

Applying the principle of homogeneity of dimensions, we get 

a=1                                       ......(ii)a+b=0                                     .......(iii)2ab+c=0                                      ......(iv)

solving eqns. (ii), (iii) and (iv), we get a = 1, b = -1, c = 1

 From eqn. (i), [m]=FV1T

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