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

Options

A. `[Kc^(-2)]`
B. `[KF^(-2)]`
C. `[cK^(-2)]`
D. `[Fc^(-2)]`

Answer

A

Explanation

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)]`