If velocity, force and time are taken to be fundamental quantities, then the dimensional formula for mass is

Step-by-step solution

Let the quantity be Q, then, Q = f (v, F, T) Assuming that the function is the product of power functions of v, F and T, Q = Kv x F y T z ...(i) where K is a dimensionless constant of proportionality. The above equation dimensionally becomes [Q] = [LT -1 ] x [MLT -2 ] y [T] z i.e., [Q] = [M y ][L x + y T -x-2y +z ] ...(ii) ​Now Q = mass i.e., [Q] = [M] So Equation (ii) becomes [M] = [M y L x + y T -x-2y +z ] its dimensional correctness requires y = 1, x + y = 0 and - x - 2y + z = 0 which on solving yields x = -1, y