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Question: If energy \((E)\), velocity \((v)\) and force \((F)\) be taken as fundamental quantity, then what ar...

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

A

Ev2Ev^{2}

B

Ev−2Ev^{- 2}

C

Fv−1Fv^{- 1}

D

Fv−2Fv^{- 2}

Answer

Ev−2Ev^{- 2}

Explanation

Solution

Let m∝ExvyFzm \propto E^{x}v^{y}F^{z}

By substituting the following dimensions :

[E]=[ML2T−2],[v]=[LT−1],[F]=[MLT−2]\lbrack E\rbrack = \lbrack ML^{2}T^{- 2}\rbrack,\lbrack v\rbrack = \lbrack LT^{- 1}\rbrack,\lbrack F\rbrack = \lbrack MLT^{- 2}\rbrack

and by equating the both sides

x=1,y=−2,z=0x = 1,y = - 2,z = 0. So [m]=[Ev−2]\lbrack m\rbrack = \lbrack Ev^{- 2}\rbrack