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

If momentum (p), area (A) and time (T) are taken to be fundamental qua

1.	If momentum (p), area (A) and time (T) are taken to be fundamental quantities, then energy has the dimensional formula.
Answer» `(pA^(-1)T^(1)]` `[p^(2)AT]` `[pA^(-(1)/(2))T]` `[pA^((1)/(2)T)]` SOLUTION :Given, fundamental quantities are momentum (p), AREA (A) and time (T). We can write energy E as `E PROP p^(A)A^(b)T^(c)` `E= kp^(a)A^(A)T^(c)` `:. [E]=[p]^(a)[A]^(A)[T]^(c)` where K is DIMENSIONLESS constant of proportionality Dimensions of `E=[E]=[M^(1)L^(2)T^(-2)] and p]=[M^(1)L^(1)T^(-1)]` `[A]=[L^(2)]` `[T]=[T^(1)]` Putting all the dimensions, we get `M^(1)L^(2)T^(-2)=[M^(1)L^(1)T^(-1)]^(a)[L^(2)][T]^(c)` `:. M^(1)L^(2)T^(-2)=M^(a)L^(2b+b)T^(-a+c)` By comparison of power `a=1, 2b+a=2` `:.2b+1=2` `b=(1)/(2)` `-a+c=-2` `c=-2+a=-2+1=-1` Thus`\|E\|=[pA^((1)/(2))T^(-1)]`