If momentum P, area A and time T are selected as fundamental quantities then energy has the dimensional formula

Options

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

Answer

C

Explanation

`EpropP^(x)A^(y)T^(z)`
`E=k[M^(1)L^(1)T^(-1)]^(x)[L^(2)]^(y)[T^(1)]^(z)`
`[M^(1)L^(2)T^(-2)]=[M^(x)L^(x+2y)T^(x+z)]`
`x=1,y=(1)/(2),z=-1`
`E=kP^(1)A^(1//2)T^(-1)`