Question

If the energy $\left(E\right)$, velocity $\left(v\right)$ and force $\left(F\right)$ be taken as fundamental quantities, then the dimensions of mass will be

• A. $F{v}^{-2}$
• B. $F{v}^{-1}$
• C. $E{v}^{-2}$
• D. $E{v}^2$

Answer 1

The correct option is C $E{v}^{-2}$

$M={\left[E\right]}^a{\left[v\right]}^b{\left[F\right]}^c$
or, $M={\left[M{L}^2{T}^{-2}\right]}^a{\left[L{T}^{-1}\right]}^b{\left[ML{T}^{-2}\right]}^c$
Thus, $a+c=1,2a+b+c=0,-2a-b-2c=0$
Solving these, we get, $a=1,b=-2,c=0$
Thus, $m=E{v}^{-2}$