If energy (E) , velocity (v) and force (F) be taken as fundamental quantity, then what are dimension

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1.Units, Dimensions and Measurement

medium

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

A

$E{v^2}$

B

$E{v^{ - 2}}$

C

$F{v^{ - 1}}$

D

$F{v^{ - 2}}$

Solution

(b) Let $m \propto {E^x}{v^y}{F^z}$

By substituting the following dimensions :

$[E] = [M{L^2}{T^{ – 2}}],\,[v] = [L{T^{ – 1}}],\,[F] = [ML{T^{ – 2}}]$

and by equating the both sides

$x = 1,\,y = – 2,\,z = 0$. So $[m] = [E{v^{ – 2}}]$

Standard 11

Physics

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