If eneryg `E`, velocity `v` and time `t` are taken t are taken as the fundamental units, what is the dimensional formula of intensity of radiation ?

Options

A. `Ev^(-2)t^(-3)`
B. `Ev^(-1)t^(-1)`
C. `Ev^(-1)t^(-2)`
D. `Ev^(-2)t^(-2).`

Answer

A

Explanation

Here Intensity `I`= Energy per sec. per unit area.
`ML^(0)T^(-3)=E^(a)v^(b)t^(c )`
`=[ML^(2)T^(-2)]^(a)[LT^(-1)]^(b)[T]^(c )=M^(a)L^(2a+b)T^(-2a-b+c)`
`:.a=1`
`2a+b=0`
`b=-2a=-2`
`-2a-b+c=-3`
`-2+2+c=-3`
`c=-3`
`:.I=Ev^(-2)t^(-3).`
Hence correct choice is `(a)`