Class 11 NEET Physics Physical World, Units and Measurements

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