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

detailed solution

Correct option is D

Let mass m∝FaVbTc or m=kFaVbTcwhere k is a dimensionless constant and a, 19 and c are the exponents. Writing dimensions on both sides, we get ML0T0=MLT−2aLT−1b[T]cML0T0=MaLa+bT−2a−b+cApplying the principle of homogeneity of dimensions, we get a=1                                       ......(ii)a+b=0                                     .......(iii)−2a−b+c=0                                      ......(iv)solving eqns. (ii), (iii) and (iv), we get a = 1, b = -1, c = 1 From eqn. (i), [m]=FV−1T