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બળ $[F],$ પ્રવેગ $[A]$ અને સમય $[T]$ ને મૂળભૂત ભૌતિક રાશિઓ તરીકે સ્વીકારવામાં આવે છે. ઊર્જાનું પરિમાણ શોધો.
$[\mathrm{F}][\mathrm{A}][\mathrm{T}]$
$[\mathrm{F}][\mathrm{A}]\left[\mathrm{T}^{2}\right]$
$[F][\mathrm{A}]\left[\mathrm{T}^{-1}\right]$
$[\mathrm{F}]\left[\mathrm{A}^{-1}\right][\mathrm{T}]$
Solution
$\mathrm{E} \propto \mathrm{F}^{\mathrm{a}} \mathrm{A}^{\mathrm{b}} \mathrm{T}^{\mathrm{c}}$
$\left[\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{2}\right] \propto\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]^{\mathrm{a}}\left[\mathrm{LT}^{-2}\right]^{\mathrm{b}}[\mathrm{T}]^{\mathrm{c}}$
$\mathrm{a}=1$
$\mathrm{a}+\mathrm{b}=2 \Rightarrow \mathrm{b}=1$
$-2 \mathrm{a}-2 \mathrm{~b}+\mathrm{c}=-2$
$\Rightarrow \mathrm{c}=2$
$\mathrm{a}=1 \mathrm{~b}=1 \mathrm{c}=2$
$\mathrm{E} \propto[\mathrm{F}][\mathrm{A}]\left[\mathrm{T}^{2}\right]$
