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Question: If energy (E), velocity (V) and force (F), be taken as fundamental quantities, then what are the dim...

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

A

EV2\text{E}\text{V}^{2}

B

EV-2\text{E}\text{V}^{\text{-2}}

C

FV-1\text{F}\text{V}^{\text{-1}}

D

FV-2\text{F}\text{V}^{\text{-2}}

Answer

EV-2\text{E}\text{V}^{\text{-2}}

Explanation

Solution

[EV-2] = [E] [V]-2 = ML2T-2 (LT-1)-2 = M \mathbf{\lbrack}\text{E}\text{V}^{\text{-2}}\mathbf{\rbrack}\mathbf{\ }\mathbf{=}\mathbf{\ }\mathbf{\lbrack}\mathbf{E}\mathbf{\rbrack}\mathbf{\ }\mathbf{\lbrack}\mathbf{V}\mathbf{\rbrack}^{\text{-2}}\mathbf{\ }\mathbf{=}\text{ M}\text{L}^{\mathbf{2}}\mathbf{T}^{\text{-2}}\mathbf{\ }\mathbf{(}\text{L}\text{T}^{\text{-1}}\mathbf{)}^{\text{-2}}\mathbf{\ }\mathbf{=}\text{ M }