Question

If energy $E$, velocity $v$ and force $F$ be taken as fundamental quantity, what are the dimensions of mass?

• A. $\left[F{v}^{-2}\right]$
• B. $\left[F{v}^{-1}\right]$
• C. $\left[E{v}^2\right]$
• D. $\left[E{v}^{-2}\right]$

Answer 1

The correct option is D $\left[E{v}^{-2}\right]$

According to the question mass,
$m\propto E^{\alpha }{v}^{\beta }{F}^{\gamma }$
by substituting the dimensions,
$\left[M\right]={\left[M{L}^2{T}^{-2}\right]}^{\alpha }{\left[L{T}^{-1}\right]}^{\beta }{\left[ML{T}^{-2}\right]}^{\gamma }$
Comparing the power on both sides,
$\alpha +\gamma =1$
$2\alpha +\beta +\gamma =0$
$-2\alpha -\beta -2\gamma =0$
by solving above equation, we get
$\alpha =1$, $\beta =-2$ and $\gamma =0$
so,
$m\propto E{v}^{-2}{F}^0$
$\text{dimentional formula of mass}=\left[E{v}^{-2}\right]$

Final answer: (b)