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

Options

A. `(P^(1)A^(-1)T^(1))`
B. `(P^(2)A^(1)T^(1))`
C. `(P^(1)A^(-1/2)T^(1))`
D. `(P^(1)A^(1/2)T^(-1))`

Answer

D

Explanation

We know that `[P]=[MLT^(-1)]`
`[A]=[L^2]`
`implies [L]=[A^(1/2)]`
Also `[P][T]= [ML]`
`implies M= ([PT])/([L])=([PT])/([A^(1/2)])=[PTA^(-1/2)]`
Energy `=[ML^(2)T^(-2)]=[PTA^(-1/2)AT^(-2)]`
`=[PA^(1/2)T^(-1)]`.