Q. If energy ($E$), velocity ($\upsilon$) and force $(F)$ be taken as fundamental quantity, then what are the dimensions of mass
A) $E\upsilon^{2}$
B) $E\upsilon^{- 2}$
C) $F\upsilon^{- 1}$
D) $F\upsilon^{- 2}$
Explanation
Let $m\ \propto E^{x}v^{y}F^{z}$ By substituting the following dimensions: $E = \left\lbrack ML^{2}T^{- 2} \right\rbrack,\lbrack v\rbrack = \left\lbrack LT^{- 1} \right\rbrack,\lbrack F\rbrack = \lbrack MLT^{- 2}\rbrack$ and by equating the both sides $x = 1,y = - 2,z = 0.$ So $\lbrack m\rbrack = \left\lbrack Ev^{- 2} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.