Question

If energy (E), momentum (P) and force (F) are chosen as fundamental units. The dimensions of mass in new system is

• A. $E^{-1}{P}^3$
• B. $E^{-1}{P}^2$
• C. $E^{-2}{P}^2$
• D. None

Answer 1

The correct option is B $E^{-1}{P}^2$

The dimesions of $E,P$ and $F$ in terms of $M,L$ and $T$ are

$\left[E\right]=M{L}^2{T}^{-2}$
$\left[P\right]=ML{T}^{-1}$
$\left[E\right]=ML{T}^{-2}$

Let $\left[M\right]=E^a{P}^b{F}^c$

or $\left[M\right]={\left[M{L}^2{T}^{-2}\right]}^a{\left[ML{T}^{-1}\right]}^b{\left[ML{T}^{-2}\right]}^c$

Equating the powers of $M,L$ and $T$, we have $a=-1,b=2$ and $c=0$

Hence $\left[M\right]=E^{-1}{P}^2$