If momentum (p), area (A) and time (t) are taken to be fundamental quantities, then energy has the dimensional formula

Let, energy E=kpaAbt2  ……… (i)where k is a dimensionless constant of proportionality. Equating dimensions on both sides of (i), we getML2T−2=MLT−1aM∘L2T∘bM0L0Tt=M2La+2bTa+cApplying the principle of homogeneity of dimensions we geta = 1 (ii) a + 2b =2 (iii)-a + c = -2  (iv)On solving equations (ii), (iii) and (iv) we get a=1,b=12,c=−1∴[E]=p1A1/2t−1