In a system of units if force (F) , acceleration (A) and time (T) are taken as fundamental units the

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1.Units, Dimensions and Measurement

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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

A

$F{A^2}T$

B

$FA{T^2}$

C

${F^2}AT$

D

$FAT$

Solution

(b) $E = K{F^a}{A^b}{T^c}$

$\left[ {M{L^2}{T^{ – 2}}} \right] = {\left[ {ML{T^{ – 2}}} \right]^a}{\left[ {L{T^{ – 2}}} \right]^b}{\left[ T \right]^c}$

$\left[ {M{L^2}{T^{ – 2}}} \right] = \left[ {{M^a}{L^{a + b}}{T^{ – 2a – 2b + c}}} \right]$

$\therefore $ $a = 1$, $a + b = 2$ $⇒$ $b = 1$

and $ – 2a – 2b + c = – 2\;\; \Rightarrow \;c = 2$

$\therefore $ $E = KFA{T^2}$.

Standard 11

Physics

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