If the energy (E), velocity (v) and force (F) are taken as fundamental quantities, then what is the dimensional formula for mass?

Options

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

Answer

B

Explanation

`m prop E^(a) v^(b) F^c`
`[M] = [ML^(2) T^(-2) ]^(a) [LT^(-1)]^(b) [MLT^(-2)]^c`
`=[M^(a+c)L^(2a+b+c)T^(-2a-b-2c)]`
`a +c =1`
`2a +b+c=0`
`-2a +b+c =0`
`-2a -b -2c = 0`
By (ii) and (iii)
c = 0
From (i) equation
a = 1, from (ii) equation
b = -2
`[m] = [Ev^(-2)]`