Suppose speed of light (c), force (F) and kinetic energy (K) are taken as the fundamental units, then the dimensional formula for mass will be

Suppose speed of light (c), force (F) and kinetic energy (K) are taken

1.	Suppose speed of light (c), force (F) and kinetic energy (K) are taken as the fundamental units, then the dimensional formula for mass will be
Answer» `[Kc^(-2)]` `[KF^(-2)]` `[CK^(-2)]` `[Fc^(-2)]` Solution :Let`G= kc^(X)F^(y)K^(z)` Where k is a dimensionless constant. `:. [M^(1)L^(0)T^(0)]= [LT^(-1)]^(x)[MLT^(-2)]^(y)[ML^(2)T^(-2)]^(z)= [M^(y+z)L^(x+y+2z)T^(-x-2y-2z)]` Applying principle of homogeneity of dimensions y+ z= 1...(i) x+y+2z= 0...(II) -x-2y-2z= 0,..(iii) Adding (ii) and (iii)we get -y=0 or y=0 From (i) z= 1-y=1 From (ii)`x= -y-2z=0-2 :. m=c^(-2)F^(0)K^(1)= Kc^(-2)` Hence the dimensional FORMULA for mass is `[Kc^(-2)]`