If momentum (P), A. (P1 A–1 T1)

B. (P2 A1 T1)

C. (P1 A–1/2 T1)

D. (P1 A1/2 T–1)

According to question, momentum area and time are taken as fundamental quantities.

Now, we know that dimension of

Momentum(p)=

Area(A)=

Time (T)=

Energy=

Let us suppose,

E=

Now using principal of homogeneity, which states that the dimensions on both sides of a dimensional equation is same, we get

=

Equating the like terms we get

a=1, a+2b=2, -a+c=-2

1+2b=2, -1+c=-2

2b=1, c=-1

a=1, b=1/2, c=-1

Therefore,

E=