In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy is
In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy is
$F{A^2}T$
$FA{T^2}$
${F^2}AT$
$FAT$
In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy is
$E = K{F^a}{A^b}{T^c}$
$\left[ {M{L^2}{T^{ - 2}}} \right] = {\left[ {ML{T^{ - 2}}} \right]^a}{\left[ {L{T^{ - 2}}} \right]^b}{\left[ T \right]^c}$
$\left[ {M{L^2}{T^{ - 2}}} \right] = \left[ {{M^a}{L^{a + b}}{T^{ - 2a - 2b + c}}} \right]$
$\therefore $ $a = 1$, $a + b = 2$ $⇒$ $b = 1$
and $ - 2a - 2b + c = - 2\;\; \Rightarrow \;c = 2$
$\therefore $ $E = KFA{T^2}$.
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