Let k=PxSycz...(i) k is a dimensionless Dimensions of k=[M0L0T0] ∴ Dimensions of P=
Force
Area
=
[MLT−2]
[L2]
=[ML−1T−2] Dimensions of S=
Energy
Area×time
=
[ML2T−2]
[L2][T]
=[ML−3] Dimensions of c=[LT−1] Substituting these dimensions in eqn (i), we get [M0L0T0]=[ML−1T−2]x[MT−3]y[LT−1]z Applying the principle of homogeneity of dimensions, we get x+y=0...(ii) −x+z=0...(iii) −2x−3y−z=0...(iv) Solving (ii), (iii) and (iv), we get x=1,y=−1,z=1