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If the energy $(E)$ , velocity $(v)$ and force ( $F$ ) be taken as a fundamental quantities, then the dimensions of mass will be

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[Fv−2]

[Fv−1]

[Ev−2]

[Ev2]

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detailed solution

Correct option is C

Let EavbFc=km Then,[ML2T−2]a[LT−1]b[MLT−2]c=[M] [Ma+cL2a+b+cT−2a-b-2c]=[M]a+c=1---(1) 2a+b+c=0---(2) -2a-b-2c=0---(3) from (2) &(3) we get c=0 substitute in (1) we get a=1 substitute a & b values in (2) 2(1)+b+0=0 b=-2E1v-2F0=m

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If the energy (E) , velocity (v) and force (F ) be taken as a fundamental quantities, then the dimensions of mass will be

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If the energy $(E)$ , velocity $(v)$ and force ( $F$ ) be taken as a fundamental quantities, then the dimensions of mass will be