1.

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

Answer»

`[P^1 A^(-1) T^1]`
`[P^2 A^1 T^1]`
`[P^1 A^(-1//2) T^1]`
`[P^1 A^(1//2) T^(-1)]`

SOLUTION :Let energy , `E prop P^a A^b T^c`
or `E=kP^a A^b T^c`
or `[ML^2 T^(-2)]=[MLT^(-1)]^a [L^2]^b[T]^c = [M^a L^(a+2b)T^(-a+c)]`
whence , a=1 , b=`1/2` , c=-1
DIMENSIONAL FORMULA for E is `[P^1 A^(1//2) T^(-1)]`


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