If force [F], acceleration [A] and time [T] a | vedclass

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Question

$\mathrm{E} \propto \mathrm{F}^{\mathrm{a}} \mathrm{A}^{\mathrm{b}} \mathrm{T}^{\mathrm{c}}$

$\left[\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{2}\

Vedclass · Accepted Answer

$[\mathrm{F}][\mathrm{A}]\left[\mathrm{T}^{2}\right]$

Vedclass · Answer

$\mathrm{E} \propto \mathrm{F}^{\mathrm{a}} \mathrm{A}^{\mathrm{b}} \mathrm{T}^{\mathrm{c}}$

$\left[\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{2}\right] \propto\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]^{\mathrm{a}}\left[\mathrm{LT}^{-2}\right]^{\mathrm{b}}[\mathrm{T}]^{\mathrm{c}}$

$\mathrm{a}=1$

$\mathrm{a}+\mathrm{b}=2 \Rightarrow \mathrm{b}=1$

$-2 \mathrm{a}-2 \mathrm{~b}+\mathrm{c}=-2$

$\Rightarrow \mathrm{c}=2$

$\mathrm{a}=1 \mathrm{~b}=1 \mathrm{c}=2$

$\mathrm{E} \propto[\mathrm{F}][\mathrm{A}]\left[\mathrm{T}^{2}\right]$

If force $[F],$ acceleration $[A]$ and time $[T]$ are chosen as the fundamental physical quantities. Find the dimensions of energy.

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