Question

If the energy $(E)$, velocity $(v)$ and force $(F)$ be taken as fundamental quantity, then the dimension of mass will be :

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

Answer 1

Answer: (C)

Einstein by his theory of relativity, proved that mass and energy are related to each other and every substance has energy due to its mass also. If a substance loses an amount $\Delta m$ of its mass, an equivalent amount $\Delta E$ of energy is produced, where
$\Delta E=(\Delta m) c^{2}$
This is called Einstein's mass energy relation.
$\therefore $ Dimension of mass
$=\frac{\text { Dimension of energy }}{(\text { Dimension of velocity })^{2}}$
$=Ev^{-2}$
Alternative : Putting the dimensions of energy and velocity, we get
Energy $=\left[ MLT ^{-2} L \right]=\left[ ML ^{2} T ^{-2}\right]$
Velocity $ =\left[ LT ^{-1}\right] $
$\therefore \frac{\text { Energy }}{\text { (Velocity) }^{2}} =\frac{\left[ ML ^{2} T ^{-2}\right]}{\left[ L ^{2} T ^{-2}\right]}=[ M ] $
$\Rightarrow [ M ] =\left[E v^{-2}\right]$