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

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 v2

Tardigrade Admin · Accepted Answer

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

Δ m

of its mass, an equivalent amount

Δ E

of energy is produced, where

Δ E = (Δ m) c^{2}

This is called Einstein's mass energy relation.

∴

Dimension of mass

= \frac{Dimension of energy}{( Dimension of velocity ) ^{2}}

= E v^{- 2}

Alternative : Putting the dimensions of energy and velocity, we get
Energy

= [M L T^{- 2} L] = [M L^{2} T^{- 2}]

Velocity

= [L T^{- 1}]

∴ \frac{Energy}{(Velocity) ^{2}} = \frac{[ M L ^{2} T ^{- 2} ]}{[ L ^{2} T ^{- 2} ]} = [M]

\Rightarrow [M] = [E v^{- 2}]

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

$F v^{- 2}$

$F v^{- 1}$

$E v^{- 2}$

$E v^{2}$

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

Fv−2

Fv−1

Ev−2

Ev2

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

$F v^{- 2}$

$F v^{- 1}$

$E v^{- 2}$

$E v^{2}$